Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind type parameter. More...

Detailed Description

Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind type parameter.

See the documentation of setFFTR for more details.

Parameters

[in]

data

: The input contiguous vector of arbitrary size of,

type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),

containing the periodic sequence whose FFT is to be computed.

Returns: fft : The output vector of the same type, kind, and size as the input data, containing the FFT result.

Possible calling interfaces ⛓

: use pm_fftpack, only: getFFTR

fft = getFFTR(data(:))

pm_fftpack::getFFTR
Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type compl...
Definition: pm_fftpack.F90:1156

pm_fftpack
This module contains procedures and generic interfaces for computing the Discrete Fourier Transform o...
Definition: pm_fftpack.F90:205

Remarks: The procedures under discussion are impure.

Note: This functional generic interface is simply a more flexible but slower wrapper around the subroutine generic interface setFFTR.
As such, this functional interface can be significantly slower than the corresponding subroutine interface.

See also: getFFTF
getFFTR
getFFTI
setFFTF
setFFTR
setFFTI

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_io, only: display_type

5 use pm_fftpack, only: getfactorFFT

6 use pm_fftpack, only: getFFTF, getFFTR

7 use pm_distUnif, only: getUnifRand

8 use pm_mathCompare, only: isClose

9 use pm_err, only: setAsserted

10

11 implicit none

12

13 integer(IK) :: i

14 integer(IK) :: lenData

15 type(display_type) :: disp

16 disp = display_type(file = "main.out.F90")

17

18 do i = 1, 5

19 block

20 use pm_kind, only: TKC => CKS

21 real(TKC) :: reltol

22 complex(TKC), allocatable :: data(:), adat(:)

23 call disp%show("lenData = getUnifRand(5, 100)")

24 lenData = getUnifRand(5, 100)

25 call disp%show("lenData")

26 call disp%show( lenData )

27 call disp%show("data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)")

28 data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

29 call disp%show("data")

30 call disp%show( data )

31 call disp%skip()

32 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

33 adat = getFFTR(getFFTF(data)) / size(data)

34 call disp%show("adat")

35 call disp%show( adat )

36 call disp%show("reltol = sqrt(epsilon(1._TKC))")

37 reltol = sqrt(epsilon(1._TKC))

38 call disp%show("reltol")

39 call disp%show( reltol )

40 call disp%show("isClose(data, adat, reltol = reltol)")

41 call disp%show( isClose(data, adat, reltol = reltol) )

42 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

43 call setAsserted(all(isClose(data, adat, reltol = reltol)))

44 call disp%skip()

45 end block

46

47 block

48 use pm_kind, only: TKC => CKD

49 real(TKC) :: reltol

50 complex(TKC), allocatable :: data(:), adat(:)

51 call disp%show("lenData = getUnifRand(5, 100)")

52 lenData = getUnifRand(5, 100)

53 call disp%show("lenData")

54 call disp%show( lenData )

55 call disp%show("data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)")

56 data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

57 call disp%show("data")

58 call disp%show( data )

59 call disp%skip()

60 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

61 adat = getFFTR(getFFTF(data)) / size(data)

62 call disp%show("adat")

63 call disp%show( adat )

64 call disp%show("reltol = sqrt(epsilon(1._TKC))")

65 reltol = sqrt(epsilon(1._TKC))

66 call disp%show("reltol")

67 call disp%show( reltol )

68 call disp%show("isClose(data, adat, reltol = reltol)")

69 call disp%show( isClose(data, adat, reltol = reltol) )

70 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

71 call setAsserted(all(isClose(data, adat, reltol = reltol)))

72 call disp%skip()

73 end block

74

75 block

76 use pm_kind, only: TKC => CKH

77 real(TKC) :: reltol

78 complex(TKC), allocatable :: data(:), adat(:)

79 call disp%show("lenData = getUnifRand(5, 100)")

80 lenData = getUnifRand(5, 100)

81 call disp%show("lenData")

82 call disp%show( lenData )

83 call disp%show("data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)")

84 data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

85 call disp%show("data")

86 call disp%show( data )

87 call disp%skip()

88 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

89 adat = getFFTR(getFFTF(data)) / size(data)

90 call disp%show("adat")

91 call disp%show( adat )

92 call disp%show("reltol = sqrt(epsilon(1._TKC))")

93 reltol = sqrt(epsilon(1._TKC))

94 call disp%show("reltol")

95 call disp%show( reltol )

96 call disp%show("isClose(data, adat, reltol = reltol)")

97 call disp%show( isClose(data, adat, reltol = reltol) )

98 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

99 call setAsserted(all(isClose(data, adat, reltol = reltol)))

100 call disp%skip()

101 end block

102

103 block

104 use pm_kind, only: TKC => RKS

105 real(TKC) :: reltol

106 real(TKC), allocatable :: data(:), adat(:)

107 call disp%show("lenData = getUnifRand(5, 100)")

108 lenData = getUnifRand(5, 100)

109 call disp%show("lenData")

110 call disp%show( lenData )

111 call disp%show("data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)")

112 data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

113 call disp%show("data")

114 call disp%show( data )

115 call disp%skip()

116 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

117 adat = getFFTR(getFFTF(data)) / size(data)

118 call disp%show("adat")

119 call disp%show( adat )

120 call disp%show("reltol = sqrt(epsilon(1._TKC))")

121 reltol = sqrt(epsilon(1._TKC))

122 call disp%show("reltol")

123 call disp%show( reltol )

124 call disp%show("isClose(data, adat, reltol = reltol)")

125 call disp%show( isClose(data, adat, reltol = reltol) )

126 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

127 call setAsserted(all(isClose(data, adat, reltol = reltol)))

128 call disp%skip()

129 end block

130

131 block

132 use pm_kind, only: TKC => RKD

133 real(TKC) :: reltol

134 real(TKC), allocatable :: data(:), adat(:)

135 call disp%show("lenData = getUnifRand(5, 100)")

136 lenData = getUnifRand(5, 100)

137 call disp%show("lenData")

138 call disp%show( lenData )

139 call disp%show("data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)")

140 data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

141 call disp%show("data")

142 call disp%show( data )

143 call disp%skip()

144 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

145 adat = getFFTR(getFFTF(data)) / size(data)

146 call disp%show("adat")

147 call disp%show( adat )

148 call disp%show("reltol = sqrt(epsilon(1._TKC))")

149 reltol = sqrt(epsilon(1._TKC))

150 call disp%show("reltol")

151 call disp%show( reltol )

152 call disp%show("isClose(data, adat, reltol = reltol)")

153 call disp%show( isClose(data, adat, reltol = reltol) )

154 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

155 call setAsserted(all(isClose(data, adat, reltol = reltol)))

156 call disp%skip()

157 end block

158

159 block

160 use pm_kind, only: TKC => RKH

161 real(TKC) :: reltol

162 real(TKC), allocatable :: data(:), adat(:)

163 call disp%show("lenData = getUnifRand(5, 100)")

164 lenData = getUnifRand(5, 100)

165 call disp%show("lenData")

166 call disp%show( lenData )

167 call disp%show("data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)")

168 data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

169 call disp%show("data")

170 call disp%show( data )

171 call disp%skip()

172 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

173 adat = getFFTR(getFFTF(data)) / size(data)

174 call disp%show("adat")

175 call disp%show( adat )

176 call disp%show("reltol = sqrt(epsilon(1._TKC))")

177 reltol = sqrt(epsilon(1._TKC))

178 call disp%show("reltol")

179 call disp%show( reltol )

180 call disp%show("isClose(data, adat, reltol = reltol)")

181 call disp%show( isClose(data, adat, reltol = reltol) )

182 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

183 call setAsserted(all(isClose(data, adat, reltol = reltol)))

184 call disp%skip()

185 end block

186 end do

187

188end program example

pm_distUnif::getUnifRand
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Definition: pm_distUnif.F90:4106

pm_err::setAsserted
Verify the input assertion holds and if it does not, print the (optional) input message on stdout and...
Definition: pm_err.F90:735

pm_err::show
Generate and return an object of type stop_type with the user-specified input attributes.
Definition: pm_err.F90:1618

pm_fftpack::getFFTF
Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of...
Definition: pm_fftpack.F90:746

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11074

pm_mathCompare::isClose
Generate and return .true. if the two input values are sufficiently close to each other within the sp...
Definition: pm_mathCompare.F90:523

pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274

pm_err
This module contains classes and procedures for reporting and handling errors.
Definition: pm_err.F90:52

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:10962

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:28

pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:281

pm_kind::CKH
integer, parameter CKH
The scalar integer constant of intrinsic default kind, representing the highest-precision complex kin...
Definition: pm_kind.F90:477

pm_kind::CKS
integer, parameter CKS
The single-precision complex kind in Fortran mode. On most platforms, this is a 32-bit real kind.
Definition: pm_kind.F90:310

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:280

pm_kind::CKD
integer, parameter CKD
The double precision complex kind in Fortran mode. On most platforms, this is a 64-bit real kind.
Definition: pm_kind.F90:311

pm_kind::RKD
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:308

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:279

pm_kind::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind a...
Definition: pm_kind.F90:462

pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:307

pm_mathCompare
This module contains the procedures and interfaces for evaluating the relative or absolute proximity ...
Definition: pm_mathCompare.F90:205

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10228

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte_fortran_*_intel* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte_fortran_*_intel*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte_fortran_*_gnu* -o main.exe

4./main.exe

Example output ⛓
1lenData = getUnifRand(5, 100)

2lenData

3+39

4data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

5data

6(+1.08356929, +0.518832922), (+1.96379972, +0.702364862), (+1.50909567, +0.210963488), (+1.39685249, +0.846200287), (+1.14697599, +0.755403638E-1), (+1.79805183, +0.439589202), (+1.88481975, +0.716018915), (+1.25817418, +0.872671604), (+1.92505765, +0.673725009E-1), (+1.38711309, +0.430140436), (+1.88039923, +0.481874704), (+1.83933973, +0.652097821), (+1.80979967, +0.227561653), (+1.06023657, +0.925607681E-1), (+1.69312501, +0.619146228), (+1.50654769, +0.673822463), (+1.48839927, +0.288456380), (+1.47347116, +0.555782139), (+1.24731946, +0.667030513), (+1.13327765, +0.865786374), (+1.09381080, +0.583880246), (+1.35797346, +0.424217224), (+1.16741323, +0.243368328), (+1.81794047, +0.726109862), (+1.72400570, +0.565130234), (+1.69214702, +0.579384804), (+1.60093975, +0.197144687), (+1.96792042, +0.435204268), (+1.84840512, +0.686327517), (+1.67256868, +0.880569160), (+1.86401665, +0.326040804), (+1.74815452, +0.791513264), (+1.49868846, +0.278787255), (+1.14285827, +0.515904307), (+1.17182326, +0.706139982), (+1.01820958, +0.468299568), (+1.26655340, +0.558261991), (+1.57850122, +0.231405497), (+1.47031736, +0.761608422)

7

8adat = getFFTR(getFFTF(data)) / size(data)

9adat

10(+1.08356929, +0.518832862), (+1.96379983, +0.702364802), (+1.50909579, +0.210963413), (+1.39685261, +0.846200287), (+1.14697599, +0.755404234E-1), (+1.79805183, +0.439589024), (+1.88481998, +0.716018975), (+1.25817478, +0.872671783), (+1.92505741, +0.673723966E-1), (+1.38711309, +0.430140465), (+1.88039947, +0.481874704), (+1.83933997, +0.652097821), (+1.80979979, +0.227561533), (+1.06023633, +0.925608203E-1), (+1.69312501, +0.619146228), (+1.50654793, +0.673822463), (+1.48839927, +0.288456410), (+1.47347116, +0.555782199), (+1.24731946, +0.667030454), (+1.13327789, +0.865786433), (+1.09381115, +0.583880305), (+1.35797346, +0.424217284), (+1.16741335, +0.243368343), (+1.81794071, +0.726109922), (+1.72400582, +0.565130293), (+1.69214714, +0.579384804), (+1.60093951, +0.197144538), (+1.96792078, +0.435204238), (+1.84840512, +0.686327636), (+1.67256868, +0.880569160), (+1.86401665, +0.326040804), (+1.74815428, +0.791513205), (+1.49868870, +0.278787404), (+1.14285851, +0.515904367), (+1.17182314, +0.706139922), (+1.01820958, +0.468299538), (+1.26655352, +0.558261991), (+1.57850134, +0.231405556), (+1.47031748, +0.761608362)

11reltol = sqrt(epsilon(1._TKC))

12reltol

13+0.345266977E-3

14isClose(data, adat, reltol = reltol)

15T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

16call setAsserted(all(isClose(data, adat, reltol = reltol)))

17

18lenData = getUnifRand(5, 100)

19lenData

20+96

21data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

22data

23(+1.4655976526128152, +0.48228328426556955), (+1.8117489534597144, +0.76917924399592330), (+1.5035868959489154, +0.24390857679208000), (+1.5265094763175819, +0.37551091102438150E-1), (+1.8120798930752495, +0.70271424608026090), (+1.0435087246356805, +0.26003795394955287), (+1.8222028264565577, +0.47130826766926182), (+1.4519743175338409, +0.18866117159163198E-1), (+1.6588011616251668, +0.87935947896750910), (+1.9358480351146850, +0.20241002374882355E-1), (+1.5064247047241679, +0.42577017383009419), (+1.7070633865392417, +0.86087682225813023), (+1.8289756527103065, +0.47989714823373064), (+1.7757923931189197, +0.25054332706706539E-1), (+1.7273166833582942, +0.31485885777302980), (+1.4869374437932277, +0.49378667370298668), (+1.7012774080281310, +0.41369752759492651), (+1.6220333935163715, +0.25232126474613059), (+1.5751923878778435, +0.93224495212085001), (+1.7211432424216406, +0.66184027617749641), (+1.0803810531847924, +0.44563603656349049), (+1.4549553777364337, +0.86395985142106146), (+1.8863417207109132, +0.44695845114130572), (+1.3197931462351455, +0.35781151378864595), (+1.3591977433903328, +0.53667221722994973), (+1.4261980370225944, +0.31296198508487294), (+1.5387915003632440, +0.17283279312064548), (+1.1206812059526055, +0.94206930974452985), (+1.5145156336069094, +0.72805697251167589E-1), (+1.7601892766833325, +0.24434324146867947), (+1.0201092816762842, +0.65805283968738570), (+1.8713851918656139, +0.26838741368140684E-1), (+1.1535182208588295, +0.68671216663472823), (+1.1763138651514553, +0.68503427463387034), (+1.3588128540225137, +0.38607063534750985), (+1.4592650898946549, +0.14716372457301163), (+1.8118356550566226, +0.92130871776056145), (+1.1052347032250593, +0.30713976619684291), (+1.4286440415673960, +0.74937742301763610), (+1.2186649622214030, +0.29244508137998837E-1), (+1.4182565540566265, +0.15924646108355534), (+1.9850493120554442, +0.97566392960502946), (+1.0070334097476121, +0.65533568610547477), (+1.2077252609731626, +0.54379245664517284), (+1.4390305320728090, +0.91447007016614823), (+1.6901026746465284, +0.36998847363839871), (+1.9483968494590687, +0.65398720080951589), (+1.1733758557305058, +0.90889003837636417), (+1.7996360459268479, +0.62802012733305468), (+1.2381426178837867, +0.22032729984624411), (+1.7919621004906485, +0.70628507004713803), (+1.1316790602715412, +0.79975178303712757), (+1.2278340602512037, +0.53507841373872045), (+1.6314923240445425, +0.20842848896914579), (+1.2300630768642091, +0.37362935868686153), (+1.4745054249709608, +0.98276893766830131E-1), (+1.6945444063348083, +0.64689935636852203), (+1.0365899784140651, +0.86435193889595940), (+1.0224358400703610, +0.27487779260232348), (+1.5873804825634230, +0.77137127700445196), (+1.2380106499019534, +0.90297431701562736), (+1.6621017685497002, +0.15852469743175068), (+1.4085837420730372, +0.45340191409180219), (+1.9097931443951790, +0.50641085576989264), (+1.2361415750931015, +0.17452769980775096), (+1.8600065838650557, +0.87381289218595459), (+1.0682580547955252, +0.82527002383879899), (+1.9697530137747390, +0.10100508645886730), (+1.9448701685388126, +0.75543667894276834), (+1.2861460705101684, +0.25358264536132913), (+1.3581200447895649, +0.29610934881498163), (+1.9940033904894232, +0.70699814454111110), (+1.9236833207983639, +0.14879362002177754), (+1.8711747078921741, +0.49771290312043115), (+1.5092752050556024, +0.26563050592814885), (+1.9404252506322264, +0.10937066205378310), (+1.7748885818671740, +0.19697536616636802), (+1.3303504929336016, +0.16050788947501382), (+1.1853927035969436, +0.45978054771485866E-1), (+1.8501003938076133, +0.76387915026368025), (+1.0133100827251114, +0.43902870027306173), (+1.2146039979999665, +0.11593224183726347), (+1.2122188399040010, +0.22954331448397602), (+1.6122907223642517, +0.11225035325292954E-2), (+1.5202394124350049, +0.19286847722306799), (+1.3538661378322834, +0.49622798570405513), (+1.2018384536542386, +0.27243375951515381E-1), (+1.2424253769246558, +0.57534143650747893), (+1.1390752024320792, +0.32070421002229177), (+1.9952335401880781, +0.27969877930773512), (+1.6627763414866878, +0.64955129831179903E-1), (+1.9597372174896976, +0.99287052148021337), (+1.4912980075007334, +0.57518930013610636), (+1.4179961206733505, +0.10648955693059614), (+1.7868548312600252, +0.91697097893097002), (+1.6773348835596951, +0.14360992282802543)

24

25adat = getFFTR(getFFTF(data)) / size(data)

26adat

27(+1.4655976526128149, +0.48228328426556949), (+1.8117489534597144, +0.76917924399592319), (+1.5035868959489154, +0.24390857679208011), (+1.5265094763175824, +0.37551091102438004E-1), (+1.8120798930752497, +0.70271424608026090), (+1.0435087246356802, +0.26003795394955309), (+1.8222028264565575, +0.47130826766926176), (+1.4519743175338411, +0.18866117159163170E-1), (+1.6588011616251663, +0.87935947896750910), (+1.9358480351146852, +0.20241002374882317E-1), (+1.5064247047241679, +0.42577017383009425), (+1.7070633865392424, +0.86087682225813011), (+1.8289756527103063, +0.47989714823373059), (+1.7757923931189203, +0.25054332706706556E-1), (+1.7273166833582938, +0.31485885777302997), (+1.4869374437932279, +0.49378667370298662), (+1.7012774080281308, +0.41369752759492645), (+1.6220333935163715, +0.25232126474613037), (+1.5751923878778438, +0.93224495212084990), (+1.7211432424216409, +0.66184027617749630), (+1.0803810531847919, +0.44563603656349055), (+1.4549553777364341, +0.86395985142106158), (+1.8863417207109130, +0.44695845114130567), (+1.3197931462351453, +0.35781151378864590), (+1.3591977433903331, +0.53667221722994951), (+1.4261980370225944, +0.31296198508487283), (+1.5387915003632440, +0.17283279312064559), (+1.1206812059526059, +0.94206930974452963), (+1.5145156336069094, +0.72805697251167770E-1), (+1.7601892766833325, +0.24434324146867945), (+1.0201092816762840, +0.65805283968738559), (+1.8713851918656141, +0.26838741368140722E-1), (+1.1535182208588295, +0.68671216663472823), (+1.1763138651514555, +0.68503427463387023), (+1.3588128540225137, +0.38607063534750991), (+1.4592650898946546, +0.14716372457301150), (+1.8118356550566228, +0.92130871776056156), (+1.1052347032250598, +0.30713976619684308), (+1.4286440415673958, +0.74937742301763632), (+1.2186649622214034, +0.29244508137999059E-1), (+1.4182565540566265, +0.15924646108355534), (+1.9850493120554440, +0.97566392960502935), (+1.0070334097476124, +0.65533568610547455), (+1.2077252609731628, +0.54379245664517251), (+1.4390305320728090, +0.91447007016614812), (+1.6901026746465286, +0.36998847363839876), (+1.9483968494590684, +0.65398720080951611), (+1.1733758557305054, +0.90889003837636384), (+1.7996360459268477, +0.62802012733305468), (+1.2381426178837867, +0.22032729984624413), (+1.7919621004906485, +0.70628507004713803), (+1.1316790602715419, +0.79975178303712768), (+1.2278340602512037, +0.53507841373872056), (+1.6314923240445423, +0.20842848896914579), (+1.2300630768642089, +0.37362935868686148), (+1.4745054249709606, +0.98276893766830284E-1), (+1.6945444063348081, +0.64689935636852181), (+1.0365899784140655, +0.86435193889595940), (+1.0224358400703608, +0.27487779260232348), (+1.5873804825634235, +0.77137127700445207), (+1.2380106499019534, +0.90297431701562736), (+1.6621017685497008, +0.15852469743175077), (+1.4085837420730367, +0.45340191409180242), (+1.9097931443951790, +0.50641085576989264), (+1.2361415750931013, +0.17452769980775110), (+1.8600065838650561, +0.87381289218595448), (+1.0682580547955256, +0.82527002383879910), (+1.9697530137747392, +0.10100508645886715), (+1.9448701685388123, +0.75543667894276834), (+1.2861460705101688, +0.25358264536132918), (+1.3581200447895647, +0.29610934881498180), (+1.9940033904894232, +0.70699814454111098), (+1.9236833207983637, +0.14879362002177754), (+1.8711747078921741, +0.49771290312043109), (+1.5092752050556022, +0.26563050592814880), (+1.9404252506322266, +0.10937066205378287), (+1.7748885818671740, +0.19697536616636815), (+1.3303504929336014, +0.16050788947501363), (+1.1853927035969438, +0.45978054771485942E-1), (+1.8501003938076133, +0.76387915026368025), (+1.0133100827251114, +0.43902870027306179), (+1.2146039979999668, +0.11593224183726343), (+1.2122188399040010, +0.22954331448397602), (+1.6122907223642515, +0.11225035325290362E-2), (+1.5202394124350052, +0.19286847722306813), (+1.3538661378322840, +0.49622798570405524), (+1.2018384536542384, +0.27243375951515453E-1), (+1.2424253769246560, +0.57534143650747893), (+1.1390752024320792, +0.32070421002229166), (+1.9952335401880781, +0.27969877930773496), (+1.6627763414866881, +0.64955129831179972E-1), (+1.9597372174896979, +0.99287052148021326), (+1.4912980075007336, +0.57518930013610647), (+1.4179961206733507, +0.10648955693059597), (+1.7868548312600250, +0.91697097893097013), (+1.6773348835596951, +0.14360992282802543)

28reltol = sqrt(epsilon(1._TKC))

29reltol

30+0.14901161193847656E-7

31isClose(data, adat, reltol = reltol)

32T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

33call setAsserted(all(isClose(data, adat, reltol = reltol)))

34

35lenData = getUnifRand(5, 100)

36lenData

37+71

38data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

39data

40(+1.72385443087335944512728230450797282, +0.417590073751874784359287970250239163), (+1.83448174136125808923450173929043102, +0.358474715066451142795251177385883461), (+1.17450646221064003056610543201458155, +0.963878515536836740292453361235559383), (+1.23919769492132365312405603738979377, +0.427156769682158723071356471303924308), (+1.00626629245723141398247523817974525, +0.469702179812798117342847258550585256E-1), (+1.49589755404625999583433241543137459, +0.262977018271381551072506245490774018), (+1.55964971609702469282055533993741894, +0.381036544730349209135913235540624770), (+1.51388140433187003260401225251770831, +0.210059752380431006174001390670653178), (+1.02994374731554272404132175424693944, +0.285196033882231974236564873362594383E-1), (+1.71131177754141035393539823492695240, +0.968620723658555088549950039790185238E-1), (+1.79818062356797409974703480388245908, +0.786613870474308058842992393278048293E-1), (+1.54210073909141170756120671663462510, +0.647820734412813099242342091732015529), (+1.65026731920965168478341628574695356, +0.839545555811287038674427462870642399), (+1.64820967527578761840529772245299591, +0.764343000491756304683322296554709853), (+1.71585762085005938983758018287324702, +0.719939351960420646204651049175555709E-2), (+1.72178251434199765370586474291162108, +0.449236190160098365197240970727010899), (+1.34346571479494088318975061314247261, +0.429598426563011008540307052148903447E-2), (+1.06940853564847826129696192110169787, +0.838283303900873922131771900847292894), (+1.61181134937572715653070445345104452, +0.261963889980126901146986747768017290), (+1.54986246848598879138168874815728935, +0.630447475059014861676168847614453384), (+1.52184037915576545408721507901562072, +0.808009518585797683122562467145675028), (+1.16332183073273289014174809250028008, +0.232169689210299157314816649896602181), (+1.89227507447756371247709976696008247, +0.744346898371815079410936336117808122), (+1.13447828540874671193635097443833778, +0.264279655395860035642776892634179294E-1), (+1.41922095118548251368482288210177083, +0.761352127717539683332660032972234345), (+1.49310862006079751241547489811036165, +0.161042031496270220289649536657917495), (+1.97177043509854902919558546570682236, +0.404876680621316081120318205966599468), (+1.93697887765660673709490412052026196, +0.923185486612445011397171128323270715), (+1.79078975272730710967598532018116425, +0.374101305939581939676437715028276781), (+1.93010094075425715207074744039575586, +0.316002115393775562504090859864837628), (+1.18576769354883293715666129931084040, +0.670409839053678501056525294827932540), (+1.42071768454179660123861818266324990, +0.379214427132999698365040268982382136), (+1.67814118744909568356682789694382928, +0.663263166542089989243124586742453879), (+1.30933369085125014434919838155144835, +0.719327076589832751549696819021874519), (+1.79517126834565020813944280342574572, +0.864394915852244604936294666625090410), (+1.76407415397974035250001474261715866, +0.861965125134916107433474919747466265), (+1.07622400352791935332675724740456849, +0.979187160737968931042124782905383375E-1), (+1.50800481611387181197948119087856286, +0.275870114548181616451840136856658478), (+1.91665566273274634196251843258029010, +0.588939270006217157167117693820904039), (+1.82173766473262370892974862727853056, +0.351415219834731807915219690116039323), (+1.80682529981941127695240505082157594, +0.791675341133630827544759957997221187), (+1.49473312809753831105271749252651538, +0.445392488086601232416765096335506560), (+1.45399844319071539656875447239653702, +0.679000618412433930419951567467849588), (+1.42477848892647746355949158079065078, +0.304119664212720674725726028221334679), (+1.19230562070333526732813172864636199, +0.981813756972949887063802261518468038), (+1.44401083277672460583348637595951014, +0.255525071086213000191009739367545543), (+1.14815612759433096830378682607647233, +0.876789720779789712525237337957736825), (+1.88478820902512619702829092804015715, +0.981481376617140303565466490018121787E-1), (+1.80933896765692143668734462688805773, +0.358665244221801831969194130360799512), (+1.16097435445447599465436487932525318, +0.110234907150579616432117140774667716), (+1.65851981953220256674433512187535735, +0.741494253556598364114114472129587316), (+1.29657413480093844813937873281072199, +0.367068106358225719692495175340526031), (+1.22743003150154980834560218679659668, +0.501891991833702518328505499422948593), (+1.53529052552847913345182829505701944, +0.178629232258646219843120554266780431), (+1.89004280540159741419151556255679489, +0.602522166678725482142885306503156524E-1), (+1.76168266558257303535644202036357549, +0.619311450948922940119408122889023819), (+1.35824904649502784171137400524699133, +0.442077535501667865985016621478496599), (+1.68699792128001509187112434550481474, +0.708501717006114199315830959791134511), (+1.92629865551556166487759934049330986, +0.877270382365537403089990810351135689), (+1.75939078494176024917088121178140225, +0.468474707997910548660909212167633146), (+1.78687049187857174183591526475242499, +0.592889677146739596997439841594649273), (+1.49258216392787850103713605706982901, +0.278407131107097861137338776737136589), (+1.12819851528226971034552470495245314, +0.198165799228895603603886241215436034), (+1.94722992386366988355337499805230538, +0.289489940793527442671751589311998151), (+1.05464283485283273266935993981913032, +0.741331992467709196654490850397072682), (+1.80705225248353718986937971779880318, +0.160590392204030680436135114799299492), (+1.39829415526870735053995606129154693, +0.210805290732185915971458804929825647), (+1.56496453350081203588872538484189368, +0.271142089534839503818768370672751066), (+1.60447164857503563586507454037713037, +0.796475034608070328218543190808154742), (+1.60234048419667581807693724067011239, +0.232907649035923009803879322238335778), (+1.53507461459785655137039964851470854, +0.514431645592486067699520741997555423)

41

42adat = getFFTR(getFFTF(data)) / size(data)

43adat

44(+1.72385443087335944512728230450797302, +0.417590073751874784359287970250239356), (+1.83448174136125808923450173929043083, +0.358474715066451142795251177385883317), (+1.17450646221064003056610543201458155, +0.963878515536836740292453361235559576), (+1.23919769492132365312405603738979396, +0.427156769682158723071356471303924308), (+1.00626629245723141398247523817974506, +0.469702179812798117342847258550584353E-1), (+1.49589755404625999583433241543137440, +0.262977018271381551072506245490773873), (+1.55964971609702469282055533993741856, +0.381036544730349209135913235540624770), (+1.51388140433187003260401225251770831, +0.210059752380431006174001390670653274), (+1.02994374731554272404132175424693847, +0.285196033882231974236564873362593721E-1), (+1.71131177754141035393539823492695143, +0.968620723658555088549950039790183914E-1), (+1.79818062356797409974703480388245889, +0.786613870474308058842992393278049377E-1), (+1.54210073909141170756120671663462471, +0.647820734412813099242342091732016011), (+1.65026731920965168478341628574695336, +0.839545555811287038674427462870642591), (+1.64820967527578761840529772245299610, +0.764343000491756304683322296554709756), (+1.71585762085005938983758018287324683, +0.719939351960420646204651049175542167E-2), (+1.72178251434199765370586474291162108, +0.449236190160098365197240970727010899), (+1.34346571479494088318975061314247242, +0.429598426563011008540307052148889077E-2), (+1.06940853564847826129696192110169749, +0.838283303900873922131771900847293183), (+1.61181134937572715653070445345104355, +0.261963889980126901146986747768017435), (+1.54986246848598879138168874815728858, +0.630447475059014861676168847614453191), (+1.52184037915576545408721507901562072, +0.808009518585797683122562467145675124), (+1.16332183073273289014174809250027969, +0.232169689210299157314816649896602085), (+1.89227507447756371247709976696008285, +0.744346898371815079410936336117808026), (+1.13447828540874671193635097443833740, +0.264279655395860035642776892634177489E-1), (+1.41922095118548251368482288210177064, +0.761352127717539683332660032972234056), (+1.49310862006079751241547489811036127, +0.161042031496270220289649536657917615), (+1.97177043509854902919558546570682139, +0.404876680621316081120318205966599324), (+1.93697887765660673709490412052026177, +0.923185486612445011397171128323271004), (+1.79078975272730710967598532018116386, +0.374101305939581939676437715028276637), (+1.93010094075425715207074744039575509, +0.316002115393775562504090859864837676), (+1.18576769354883293715666129931084021, +0.670409839053678501056525294827932155), (+1.42071768454179660123861818266324933, +0.379214427132999698365040268982382088), (+1.67814118744909568356682789694382831, +0.663263166542089989243124586742453782), (+1.30933369085125014434919838155144739, +0.719327076589832751549696819021874423), (+1.79517126834565020813944280342574495, +0.864394915852244604936294666625090217), (+1.76407415397974035250001474261715769, +0.861965125134916107433474919747466072), (+1.07622400352791935332675724740456772, +0.979187160737968931042124782905382291E-1), (+1.50800481611387181197948119087856190, +0.275870114548181616451840136856658189), (+1.91665566273274634196251843258028952, +0.588939270006217157167117693820904136), (+1.82173766473262370892974862727852959, +0.351415219834731807915219690116039179), (+1.80682529981941127695240505082157536, +0.791675341133630827544759957997221090), (+1.49473312809753831105271749252651500, +0.445392488086601232416765096335506463), (+1.45399844319071539656875447239653625, +0.679000618412433930419951567467849395), (+1.42477848892647746355949158079065059, +0.304119664212720674725726028221334583), (+1.19230562070333526732813172864636180, +0.981813756972949887063802261518468423), (+1.44401083277672460583348637595950918, +0.255525071086213000191009739367545446), (+1.14815612759433096830378682607647175, +0.876789720779789712525237337957736825), (+1.88478820902512619702829092804015695, +0.981481376617140303565466490018120584E-1), (+1.80933896765692143668734462688805754, +0.358665244221801831969194130360799416), (+1.16097435445447599465436487932525318, +0.110234907150579616432117140774667836), (+1.65851981953220256674433512187535677, +0.741494253556598364114114472129587124), (+1.29657413480093844813937873281072180, +0.367068106358225719692495175340526031), (+1.22743003150154980834560218679659610, +0.501891991833702518328505499422948208), (+1.53529052552847913345182829505701867, +0.178629232258646219843120554266780575), (+1.89004280540159741419151556255679450, +0.602522166678725482142885306503157366E-1), (+1.76168266558257303535644202036357510, +0.619311450948922940119408122889023915), (+1.35824904649502784171137400524699133, +0.442077535501667865985016621478496695), (+1.68699792128001509187112434550481493, +0.708501717006114199315830959791134704), (+1.92629865551556166487759934049330986, +0.877270382365537403089990810351135593), (+1.75939078494176024917088121178140225, +0.468474707997910548660909212167633002), (+1.78687049187857174183591526475242479, +0.592889677146739596997439841594649658), (+1.49258216392787850103713605706982862, +0.278407131107097861137338776737136445), (+1.12819851528226971034552470495245199, +0.198165799228895603603886241215436010), (+1.94722992386366988355337499805230423, +0.289489940793527442671751589311998199), (+1.05464283485283273266935993981913032, +0.741331992467709196654490850397072682), (+1.80705225248353718986937971779880299, +0.160590392204030680436135114799299420), (+1.39829415526870735053995606129154674, +0.210805290732185915971458804929825503), (+1.56496453350081203588872538484189387, +0.271142089534839503818768370672751162), (+1.60447164857503563586507454037713057, +0.796475034608070328218543190808154549), (+1.60234048419667581807693724067011239, +0.232907649035923009803879322238336019), (+1.53507461459785655137039964851470873, +0.514431645592486067699520741997555231)

45reltol = sqrt(epsilon(1._TKC))

46reltol

47+0.138777878078144567552953958511352539E-16

48isClose(data, adat, reltol = reltol)

49T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

50call setAsserted(all(isClose(data, adat, reltol = reltol)))

51

52lenData = getUnifRand(5, 100)

53lenData

54+68

55data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

56data

57+1.98385394, +1.25087714, +1.70530128, +1.12171090, +1.69923663, +1.45908117, +1.59164870, +1.62178040, +1.80572534, +1.31661773, +1.92177224, +1.56155705, +1.82531857, +1.24892974, +1.69559801, +1.48204720, +1.65735853, +1.97691464, +1.61130965, +1.99816775, +1.03730202, +1.47535586, +1.39177275, +1.00181150, +1.44123912, +1.87426138, +1.04753423, +1.97428095, +1.25909996, +1.95034111, +1.50469136, +1.09827363, +1.19935799, +1.19625211, +1.72237825, +1.53955698, +1.02667773, +1.67495704, +1.73900330, +1.90064764, +1.04972959, +1.12391484, +1.01044893, +1.81417942, +1.69288576, +1.43115175, +1.30798852, +1.94204044, +1.10136747, +1.06492829, +1.68247080, +1.03068018, +1.76064563, +1.85211194, +1.33214021, +1.80377603, +1.32408023, +1.81202292, +1.15758646, +1.10074353, +1.02118611, +1.07652020, +1.98403382, +1.97790551, +1.37505889, +1.26991725, +1.28844380, +1.27570987

58

59adat = getFFTR(getFFTF(data)) / size(data)

60adat

61+1.98385417, +1.25087690, +1.70530128, +1.12171078, +1.69923687, +1.45908117, +1.59164906, +1.62178051, +1.80572534, +1.31661749, +1.92177200, +1.56155682, +1.82531857, +1.24892938, +1.69559789, +1.48204708, +1.65735841, +1.97691393, +1.61130965, +1.99816716, +1.03730237, +1.47535574, +1.39177287, +1.00181174, +1.44123912, +1.87426126, +1.04753447, +1.97428060, +1.25910008, +1.95034075, +1.50469136, +1.09827375, +1.19935775, +1.19625199, +1.72237790, +1.53955674, +1.02667761, +1.67495656, +1.73900282, +1.90064728, +1.04972994, +1.12391484, +1.01044917, +1.81417942, +1.69288564, +1.43115163, +1.30798852, +1.94204021, +1.10136795, +1.06492817, +1.68247080, +1.03068054, +1.76064539, +1.85211122, +1.33214021, +1.80377543, +1.32408023, +1.81202245, +1.15758646, +1.10074365, +1.02118611, +1.07651997, +1.98403370, +1.97790504, +1.37505913, +1.26991737, +1.28844404, +1.27571011

62reltol = sqrt(epsilon(1._TKC))

63reltol

64+0.345266977E-3

65isClose(data, adat, reltol = reltol)

66T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

67call setAsserted(all(isClose(data, adat, reltol = reltol)))

68

69lenData = getUnifRand(5, 100)

70lenData

71+80

72data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

73data

74+1.4226455593433824, +1.1887726380950352, +1.5650533900511823, +1.5199165588534367, +1.0762318017219070, +1.2698589254903148, +1.8650820472283052, +1.1128663655868354, +1.3692939369176624, +1.9744841183317758, +1.2500357720486956, +1.8169006680761104, +1.7718146480087358, +1.9162945338350394, +1.7983414603807184, +1.5738271589557444, +1.9157690356051007, +1.3470716930570887, +1.5045975791404538, +1.4771742467639140, +1.3794426293184721, +1.6548184469438141, +1.6586780990256780, +1.7965878028377458, +1.6411565954175469, +1.0457125048679707, +1.9300562298302992, +1.0786387068348038, +1.3361596493050574, +1.1217876901814279, +1.9937689406770824, +1.5373048070794701, +1.4859690403179193, +1.8200932599202044, +1.9232634889526368, +1.4940131172557520, +1.9027618420596513, +1.5582287952849430, +1.4878478791036835, +1.8349616517901972, +1.9434810507723177, +1.1299000311701808, +1.6696076316438808, +1.0975945911692795, +1.7407261288494862, +1.7356042417247859, +1.0500227471904686, +1.0163927776605348, +1.4127371729978608, +1.4213761974119861, +1.1808388743007192, +1.2663412432505705, +1.8213433840917088, +1.9995178127040565, +1.0566617570750192, +1.8163666942127961, +1.7783935579087589, +1.4590818961108858, +1.5301333308083758, +1.4070063787011020, +1.7872928084455419, +1.1892751776741513, +1.5091216840343737, +1.3818756103364824, +1.8425809849446906, +1.1591164831367793, +1.7628083017223355, +1.6464084768690139, +1.6979703931615937, +1.6098715567471111, +1.5911976221547359, +1.0188127188430285, +1.8791222640197498, +1.0740882475829550, +1.7556471218378535, +1.9525454936527225, +1.0724581477657251, +1.1941734013996586, +1.5432829856181831, +1.6200764572663440

75

76adat = getFFTR(getFFTF(data)) / size(data)

77adat

78+1.4226455593433827, +1.1887726380950352, +1.5650533900511827, +1.5199165588534371, +1.0762318017219075, +1.2698589254903152, +1.8650820472283052, +1.1128663655868356, +1.3692939369176627, +1.9744841183317761, +1.2500357720486961, +1.8169006680761111, +1.7718146480087360, +1.9162945338350401, +1.7983414603807186, +1.5738271589557447, +1.9157690356051007, +1.3470716930570887, +1.5045975791404538, +1.4771742467639137, +1.3794426293184721, +1.6548184469438141, +1.6586780990256778, +1.7965878028377458, +1.6411565954175469, +1.0457125048679707, +1.9300562298302992, +1.0786387068348040, +1.3361596493050574, +1.1217876901814283, +1.9937689406770822, +1.5373048070794701, +1.4859690403179195, +1.8200932599202044, +1.9232634889526365, +1.4940131172557523, +1.9027618420596510, +1.5582287952849427, +1.4878478791036838, +1.8349616517901972, +1.9434810507723175, +1.1299000311701806, +1.6696076316438806, +1.0975945911692795, +1.7407261288494862, +1.7356042417247859, +1.0500227471904684, +1.0163927776605350, +1.4127371729978611, +1.4213761974119858, +1.1808388743007192, +1.2663412432505707, +1.8213433840917084, +1.9995178127040560, +1.0566617570750192, +1.8163666942127961, +1.7783935579087586, +1.4590818961108858, +1.5301333308083758, +1.4070063787011020, +1.7872928084455419, +1.1892751776741517, +1.5091216840343735, +1.3818756103364824, +1.8425809849446906, +1.1591164831367791, +1.7628083017223353, +1.6464084768690139, +1.6979703931615937, +1.6098715567471111, +1.5911976221547355, +1.0188127188430287, +1.8791222640197500, +1.0740882475829547, +1.7556471218378533, +1.9525454936527225, +1.0724581477657249, +1.1941734013996590, +1.5432829856181827, +1.6200764572663442

79reltol = sqrt(epsilon(1._TKC))

80reltol

81+0.14901161193847656E-7

82isClose(data, adat, reltol = reltol)

83T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

84call setAsserted(all(isClose(data, adat, reltol = reltol)))

85

86lenData = getUnifRand(5, 100)

87lenData

88+41

89data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

90data

91+1.08719651897371042077339330647544118, +1.60733001522594246904639936044006448, +1.98244771757024416682677346027732498, +1.03378448241180445076066711298823228, +1.75867176718153781235228762973233373, +1.83772686681154143367566527915944316, +1.84988534162719524146694612929931839, +1.97119922090335798519869477405409674, +1.17522166574835624748826432359166684, +1.79949412196849994996080108065743092, +1.92017369257924368758890219335451882, +1.74820700506395481021358123727013614, +1.21451459990953205635440846818465557, +1.67750391014487800705991403453356198, +1.25607488283788548655395215909925839, +1.56359683874504841879174229565696497, +1.39844182249450732702519500729525420, +1.18190595062088610504920113814591623, +1.39805432858123806511940365655015580, +1.48811563071940819078305168250716936, +1.18578718998050130127054754606531573, +1.26121844433886645156266788927769677, +1.75547998043737012828419439103495030, +1.03820968932824026691219762739185524, +1.54328249970001941560823011997552084, +1.70016241702801303824689561029380547, +1.51994849793205868782777314820117279, +1.42662610475094606139244003070726082, +1.73717956533452131764495554929477000, +1.87540476790914985535627410228839688, +1.64918387306570088522475859580473298, +1.83737998575008919554590629795558160, +1.19004880677788174284609007271086042, +1.22870861229213082958842062331622281, +1.81069907540414646717450746728122489, +1.64109557621467169358403479987591846, +1.75607018947586568628340128393900396, +1.27698032996560703563611758273878151, +1.06418782335536863090770933193116061, +1.91294576180169802936564498321803518, +1.62342480065351982399813367244105409

92

93adat = getFFTR(getFFTF(data)) / size(data)

94adat

95+1.08719651897371042077339330647543945, +1.60733001522594246904639936044006371, +1.98244771757024416682677346027732479, +1.03378448241180445076066711298823074, +1.75867176718153781235228762973233450, +1.83772686681154143367566527915944374, +1.84988534162719524146694612929931936, +1.97119922090335798519869477405409847, +1.17522166574835624748826432359166299, +1.79949412196849994996080108065743246, +1.92017369257924368758890219335451959, +1.74820700506395481021358123727013903, +1.21451459990953205635440846818465095, +1.67750391014487800705991403453356526, +1.25607488283788548655395215909925454, +1.56359683874504841879174229565696671, +1.39844182249450732702519500729525420, +1.18190595062088610504920113814591354, +1.39805432858123806511940365655015695, +1.48811563071940819078305168250717244, +1.18578718998050130127054754606531361, +1.26121844433886645156266788927769484, +1.75547998043737012828419439103495858, +1.03820968932824026691219762739184850, +1.54328249970001941560823011997552257, +1.70016241702801303824689561029380739, +1.51994849793205868782777314820117201, +1.42662610475094606139244003070725812, +1.73717956533452131764495554929477116, +1.87540476790914985535627410228839823, +1.64918387306570088522475859580473240, +1.83737998575008919554590629795558391, +1.19004880677788174284609007271085850, +1.22870861229213082958842062331622108, +1.81069907540414646717450746728122566, +1.64109557621467169358403479987591923, +1.75607018947586568628340128393900551, +1.27698032996560703563611758273878113, +1.06418782335536863090770933193115984, +1.91294576180169802936564498321803518, +1.62342480065351982399813367244105332

96reltol = sqrt(epsilon(1._TKC))

97reltol

98+0.138777878078144567552953958511352539E-16

99isClose(data, adat, reltol = reltol)

100T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

101call setAsserted(all(isClose(data, adat, reltol = reltol)))

102

103lenData = getUnifRand(5, 100)

104lenData

105+26

106data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

107data

108(+1.54342055, +0.141057909), (+1.51029253, +0.782028258), (+1.72214842, +0.547582984), (+1.11924458, +0.759134829), (+1.42707467, +0.698556662), (+1.62190652, +0.496520162), (+1.55869246, +0.704373538), (+1.04553866, +0.398895502), (+1.39201629, +0.568329096), (+1.40423059, +0.541745782), (+1.93466961, +0.321916163), (+1.00628448, +0.858827114), (+1.97731197, +0.797788203), (+1.21167028, +0.635189474), (+1.88915706, +0.663337708), (+1.37569427, +0.758435607), (+1.11943245, +0.992412984), (+1.84824848, +0.700686574E-1), (+1.31227970, +0.124892950), (+1.54676974, +0.139936209), (+1.22327709, +0.624427617), (+1.10374093, +0.934941292), (+1.27794862, +0.986104727), (+1.36120701, +0.385038435), (+1.69510210, +0.701215863E-1), (+1.97705269, +0.507732213)

109

110adat = getFFTR(getFFTF(data)) / size(data)

111adat

112(+1.54342091, +0.141058058), (+1.51029217, +0.782028139), (+1.72214830, +0.547582984), (+1.11924434, +0.759134710), (+1.42707491, +0.698556781), (+1.62190640, +0.496520162), (+1.55869269, +0.704373598), (+1.04553890, +0.398895681), (+1.39201629, +0.568329036), (+1.40423059, +0.541745901), (+1.93466926, +0.321916282), (+1.00628400, +0.858827174), (+1.97731161, +0.797788203), (+1.21167064, +0.635189652), (+1.88915658, +0.663337588), (+1.37569416, +0.758435607), (+1.11943221, +0.992413163), (+1.84824836, +0.700690225E-1), (+1.31227982, +0.124893077), (+1.54676998, +0.139936075), (+1.22327733, +0.624427676), (+1.10374081, +0.934941232), (+1.27794898, +0.986104846), (+1.36120677, +0.385038495), (+1.69510186, +0.701215416E-1), (+1.97705209, +0.507732213)

113reltol = sqrt(epsilon(1._TKC))

114reltol

115+0.345266977E-3

116isClose(data, adat, reltol = reltol)

117T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

118call setAsserted(all(isClose(data, adat, reltol = reltol)))

119

120lenData = getUnifRand(5, 100)

121lenData

122+59

123data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

124data

125(+1.5611508751554866, +0.80907858821934897), (+1.4600493420354346, +0.84366457634697267), (+1.4300730366260166, +0.66708330841455743), (+1.1257656669933154, +0.53575603023459839), (+1.5949273575019762, +0.44683434654668841E-1), (+1.2918249272318287, +0.44067335559441778), (+1.4756396387365851, +0.19210254884519684), (+1.5285600120949172, +0.18546020125853313), (+1.0134158018856669, +0.74759981224042704E-1), (+1.3715702102465861, +0.54260631869740039), (+1.2364104044757651, +0.77006932825826435), (+1.0986584504880370, +0.78222324345262750), (+1.9368456883834231, +0.76675825792463670), (+1.3869207956654450, +0.67965558705798113), (+1.4293098111348739, +0.36277578839149427), (+1.6152274469435768, +0.17969142943695038), (+1.6670836124464767, +0.79004095750599834), (+1.8877902373436286, +0.51192171122380137), (+1.9217999450762648, +0.24725935989432657), (+1.3470354933507709, +0.86154410058439002), (+1.5820072926844793, +0.75212329206072015), (+1.4679280038319495, +0.90002576159179093), (+1.6375831921015194, +0.78205789057412667), (+1.6715323126304151, +0.93554270706038967), (+1.2309992407136958, +0.30596904427059823), (+1.7114164238499905, +0.93358711477311407), (+1.5848720710851700, +0.85802941321785409), (+1.0346428131200349, +0.34102979002687517), (+1.3025950960925345, +0.15020671035637267), (+1.6981501910406651, +0.11683486722567760), (+1.0877591772303612, +0.81313430498891415), (+1.3946870002614884, +0.67584261791664824), (+1.2977091543894621, +0.21403085953914247), (+1.1503289323493755, +0.13909650463921996), (+1.4008394335786005, +0.75424565530917609), (+1.0491086767470854, +0.49284018470201940), (+1.6322128878653119, +0.62136391929391865), (+1.0283821963902893, +0.76194779901951903), (+1.6268557613703081, +0.93937203014325943), (+1.9769467691840608, +0.70814856685154859), (+1.6049893892181186, +0.42073756074773483E-1), (+1.3302087692555371, +0.79539071956394758), (+1.7535262540996757, +0.15159611757409519), (+1.6397764199779292, +0.51999928801434980), (+1.1950827510860462, +0.87191023975695447), (+1.3764087043251878, +0.14514372719814239), (+1.6574291278306434, +0.69962172637315190), (+1.8860375664590070, +0.11670056146893704), (+1.9722570359078191, +0.86039708507317969), (+1.5026663552706936, +0.39858836642002182E-1), (+1.7838810175736222, +0.95962052388952279), (+1.3832540480313176, +0.16859507643048410), (+1.6366568526524814, +0.35123447107092176), (+1.7527991118535677, +0.61836993649153249), (+1.4880035898803490, +0.48261945171610565), (+1.2930084500337831, +0.72486113358669646), (+1.2292651614987178, +0.16792436663951882), (+1.2875255802899086, +0.94247960738118475E-1), (+1.9441452365018597, +0.56899958813447382)

126

127adat = getFFTR(getFFTF(data)) / size(data)

128adat

129(+1.5611508751554786, +0.80907858821934608), (+1.4600493420354348, +0.84366457634697334), (+1.4300730366260173, +0.66708330841455787), (+1.1257656669933158, +0.53575603023459861), (+1.5949273575019762, +0.44683434654668848E-1), (+1.2918249272318292, +0.44067335559441789), (+1.4756396387365851, +0.19210254884519698), (+1.5285600120949170, +0.18546020125853296), (+1.0134158018856678, +0.74759981224042524E-1), (+1.3715702102465865, +0.54260631869740039), (+1.2364104044757649, +0.77006932825826468), (+1.0986584504880370, +0.78222324345262728), (+1.9368456883834229, +0.76675825792463714), (+1.3869207956654457, +0.67965558705798135), (+1.4293098111348739, +0.36277578839149410), (+1.6152274469435766, +0.17969142943695035), (+1.6670836124464767, +0.79004095750599834), (+1.8877902373436288, +0.51192171122380159), (+1.9217999450762642, +0.24725935989432685), (+1.3470354933507700, +0.86154410058439002), (+1.5820072926844795, +0.75212329206072026), (+1.4679280038319489, +0.90002576159179082), (+1.6375831921015189, +0.78205789057412700), (+1.6715323126304149, +0.93554270706038978), (+1.2309992407136952, +0.30596904427059785), (+1.7114164238499905, +0.93358711477311407), (+1.5848720710851700, +0.85802941321785409), (+1.0346428131200336, +0.34102979002687522), (+1.3025950960925337, +0.15020671035637248), (+1.6981501910406644, +0.11683486722567717), (+1.0877591772303601, +0.81313430498891404), (+1.3946870002614873, +0.67584261791664824), (+1.2977091543894608, +0.21403085953914242), (+1.1503289323493757, +0.13909650463921974), (+1.4008394335786001, +0.75424565530917587), (+1.0491086767470845, +0.49284018470201890), (+1.6322128878653119, +0.62136391929391876), (+1.0283821963902888, +0.76194779901951926), (+1.6268557613703076, +0.93937203014325976), (+1.9769467691840610, +0.70814856685154837), (+1.6049893892181173, +0.42073756074773386E-1), (+1.3302087692555364, +0.79539071956394780), (+1.7535262540996759, +0.15159611757409547), (+1.6397764199779292, +0.51999928801434969), (+1.1950827510860460, +0.87191023975695425), (+1.3764087043251874, +0.14514372719814250), (+1.6574291278306439, +0.69962172637315234), (+1.8860375664590070, +0.11670056146893731), (+1.9722570359078191, +0.86039708507317936), (+1.5026663552706934, +0.39858836642002307E-1), (+1.7838810175736226, +0.95962052388952268), (+1.3832540480313185, +0.16859507643048402), (+1.6366568526524810, +0.35123447107092176), (+1.7527991118535677, +0.61836993649153249), (+1.4880035898803494, +0.48261945171610560), (+1.2930084500337833, +0.72486113358669635), (+1.2292651614987182, +0.16792436663951890), (+1.2875255802899088, +0.94247960738118933E-1), (+1.9441452365018601, +0.56899958813447438)

130reltol = sqrt(epsilon(1._TKC))

131reltol

132+0.14901161193847656E-7

133isClose(data, adat, reltol = reltol)

134T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

135call setAsserted(all(isClose(data, adat, reltol = reltol)))

136

137lenData = getUnifRand(5, 100)

138lenData

139+15

140data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

141data

142(+1.39998822283098718307763902710447225, +0.535062541036268487795163452348615382E-1), (+1.30992752607067510077070033995533555, +0.270220538514191481507291641978633224), (+1.62251671014128285828672220607616444, +0.151792840720992958176982544255367524), (+1.57981475244961466784479858321988824, +0.822286237079013764468769722086040215E-1), (+1.51719977892523157834218609000160713, +0.894961625429032050985338024073945018), (+1.39986623793880525960225910075941114, +0.732850451858429559848283751764935355), (+1.36098706081361713977235888718849834, +0.426102749170412297303472117026085911), (+1.61664756475939343244793576668371118, +0.675201840705416525750000984353137324), (+1.32465973756205554573791778197125603, +0.817551633141317990445302424377061872), (+1.45044509497420016494784175551601837, +0.883240509025335000652720956567452197), (+1.13479278878632652086368591597564016, +0.341062553148416712689743088420881317), (+1.23226851316277241390222936562263446, +0.711004537813218945919591793555963677), (+1.47312818145739567635990879264432099, +0.960819136965455760621136024350193285), (+1.07171706523141425532804949687835828, +0.969329049036934373656418699514310837), (+1.62324559741484607028566291438357703, +0.726164319830338542548485962238112815)

143

144adat = getFFTR(getFFTF(data)) / size(data)

145adat

146(+1.39998822283098718307763902710447186, +0.535062541036268487795163452348616164E-1), (+1.30992752607067510077070033995533574, +0.270220538514191481507291641978633272), (+1.62251671014128285828672220607616464, +0.151792840720992958176982544255367573), (+1.57981475244961466784479858321988824, +0.822286237079013764468769722086040817E-1), (+1.51719977892523157834218609000160713, +0.894961625429032050985338024073945018), (+1.39986623793880525960225910075941095, +0.732850451858429559848283751764935355), (+1.36098706081361713977235888718849815, +0.426102749170412297303472117026085911), (+1.61664756475939343244793576668371156, +0.675201840705416525750000984353137324), (+1.32465973756205554573791778197125622, +0.817551633141317990445302424377062064), (+1.45044509497420016494784175551601837, +0.883240509025335000652720956567452197), (+1.13479278878632652086368591597564035, +0.341062553148416712689743088420881365), (+1.23226851316277241390222936562263446, +0.711004537813218945919591793555963774), (+1.47312818145739567635990879264432099, +0.960819136965455760621136024350193285), (+1.07171706523141425532804949687835847, +0.969329049036934373656418699514310837), (+1.62324559741484607028566291438357684, +0.726164319830338542548485962238112911)

147reltol = sqrt(epsilon(1._TKC))

148reltol

149+0.138777878078144567552953958511352539E-16

150isClose(data, adat, reltol = reltol)

151T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

152call setAsserted(all(isClose(data, adat, reltol = reltol)))

153

154lenData = getUnifRand(5, 100)

155lenData

156+79

157data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

158data

159+1.63177145, +1.46870685, +1.37419653, +1.79480028, +1.89447641, +1.46766543, +1.80114508, +1.50444555, +1.10335445, +1.52130640, +1.69801247, +1.42621279, +1.07444334, +1.79786265, +1.37836099, +1.76594687, +1.18506896, +1.39252257, +1.37208915, +1.70048940, +1.71369910, +1.42516947, +1.57852960, +1.02100420, +1.54590309, +1.58685589, +1.61624706, +1.63212419, +1.21520472, +1.06179225, +1.62920165, +1.37501240, +1.12752485, +1.30749857, +1.18000841, +1.32041192, +1.30728424, +1.71842480, +1.15212893, +1.88530767, +1.52864552, +1.87902558, +1.56189108, +1.45222473, +1.86079633, +1.99762630, +1.29591680, +1.85215998, +1.42874670, +1.07976604, +1.85120010, +1.31017137, +1.45155311, +1.56121039, +1.35288548, +1.43746972, +1.44136548, +1.18197870, +1.96798110, +1.06760573, +1.09446967, +1.56863689, +1.15144515, +1.81912863, +1.62605691, +1.52192760, +1.24051952, +1.86563849, +1.22756457, +1.13876486, +1.33622169, +1.97678113, +1.04409671, +1.89327002, +1.66838074, +1.43629718, +1.03107154, +1.49505067, +1.94134641

160

161adat = getFFTR(getFFTF(data)) / size(data)

162adat

163+1.63176870, +1.46870553, +1.37419462, +1.79480040, +1.89447868, +1.46766317, +1.80114818, +1.50444615, +1.10334873, +1.52130854, +1.69801486, +1.42621398, +1.07443333, +1.79787314, +1.37835348, +1.76595819, +1.18505919, +1.39252424, +1.37208498, +1.70049465, +1.71370530, +1.42516398, +1.57853866, +1.02098644, +1.54591072, +1.58685815, +1.61625075, +1.63213325, +1.21519911, +1.06177783, +1.62921774, +1.37501383, +1.12751341, +1.30750406, +1.17999959, +1.32041597, +1.30727458, +1.71845019, +1.15209699, +1.88533854, +1.52862597, +1.87904882, +1.56188536, +1.45221639, +1.86080492, +1.99765074, +1.29589224, +1.85218120, +1.42874312, +1.07974339, +1.85122609, +1.31015921, +1.45155466, +1.56121612, +1.35288143, +1.43747020, +1.44136941, +1.18196428, +1.96800363, +1.06759274, +1.09446275, +1.56864643, +1.15143311, +1.81914008, +1.62605631, +1.52193022, +1.24051094, +1.86565006, +1.22755885, +1.13876224, +1.33621824, +1.97679079, +1.04408753, +1.89327657, +1.66838050, +1.43629754, +1.03106821, +1.49505019, +1.94134557

164reltol = sqrt(epsilon(1._TKC))

165reltol

166+0.345266977E-3

167isClose(data, adat, reltol = reltol)

168T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

169call setAsserted(all(isClose(data, adat, reltol = reltol)))

170

171lenData = getUnifRand(5, 100)

172lenData

173+35

174data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

175data

176+1.6988755140038969, +1.1981555533091064, +1.0468394126944032, +1.3222368071650932, +1.5773999977514954, +1.4608497186313358, +1.9439668100795957, +1.1181079045714055, +1.5185328107189797, +1.7044331396340762, +1.2735420923702701, +1.6825272845250696, +1.6862606679392129, +1.4784288059658577, +1.7970848173358134, +1.5853339467310581, +1.2665174706546987, +1.7561996046737354, +1.8031714063680175, +1.3337736418552293, +1.1285644612138692, +1.4752165036659652, +1.1045402372095863, +1.2507029226394724, +1.2954854781761007, +1.1777022733979616, +1.8453004413975873, +1.8982467955557980, +1.0583096572623583, +1.5624281842467003, +1.9285172589398178, +1.4549885340593449, +1.2736913544061430, +1.4137277489986517, +1.5019932550716386

177

178adat = getFFTR(getFFTF(data)) / size(data)

179adat

180+1.6988755140038974, +1.1981555533091068, +1.0468394126944027, +1.3222368071650932, +1.5773999977514954, +1.4608497186313361, +1.9439668100795959, +1.1181079045714051, +1.5185328107189795, +1.7044331396340762, +1.2735420923702705, +1.6825272845250703, +1.6862606679392131, +1.4784288059658579, +1.7970848173358138, +1.5853339467310577, +1.2665174706546987, +1.7561996046737356, +1.8031714063680173, +1.3337736418552288, +1.1285644612138686, +1.4752165036659655, +1.1045402372095854, +1.2507029226394715, +1.2954854781761005, +1.1777022733979621, +1.8453004413975882, +1.8982467955557982, +1.0583096572623583, +1.5624281842467005, +1.9285172589398181, +1.4549885340593451, +1.2736913544061426, +1.4137277489986515, +1.5019932550716386

181reltol = sqrt(epsilon(1._TKC))

182reltol

183+0.14901161193847656E-7

184isClose(data, adat, reltol = reltol)

185T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

186call setAsserted(all(isClose(data, adat, reltol = reltol)))

187

188lenData = getUnifRand(5, 100)

189lenData

190+43

191data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

192data

193+1.43041908818996804573715171296328274, +1.10307446802619978402610497804473429, +1.30079776651717519159521682542646346, +1.61670805118872582726872659939431898, +1.76452265374437994140704763712653151, +1.33377767244509623656120791588648207, +1.80921001213791402542422153177998999, +1.02330358926839205321178192351944664, +1.31433541761240255770435394715121482, +1.11211208940752471513381793434530075, +1.69022561578268554915664505254170332, +1.12390414416232241653593017023629639, +1.08384681300789487406861714103053847, +1.53984869385161699293547738091297854, +1.55182062554704453670899996930373667, +1.29751878644996625640801347000468316, +1.62752180025375483869067537637264272, +1.52433388023688801354622241205248351, +1.50712682125728803656837512368053160, +1.61352787350898883785904041278034355, +1.72330651814793196545325368596085608, +1.09844490017496159053866008891527813, +1.76127118085730280149767460388149766, +1.33099780305757078472435324406402843, +1.75693352037618063651535191489017240, +1.75017614441854658106860734671018062, +1.70038335821838979569144895072663397, +1.51025338516206822085096799523060718, +1.43117672777798507047740154112345281, +1.41181790638817703379207287216457680, +1.03265058958725519106912045872936003, +1.86353387198314515162145229965837317, +1.02021804104142463530150869711733304, +1.40599177460610389902250379586753417, +1.73866167185089708394028143269085913, +1.48037558884174924225423560560785751, +1.60045310366811121682631224626007756, +1.73630636514473538617453278879522413, +1.98410502340028420186579733446208229, +1.95269908463161463921130895608509499, +1.67717668039559364937025518169051577, +1.12642154390708168414980973963331663, +1.97292149545792559725339263370354428

194

195adat = getFFTR(getFFTF(data)) / size(data)

196adat

197+1.43041908818996804573715171296328408, +1.10307446802619978402610497804473487, +1.30079776651717519159521682542646403, +1.61670805118872582726872659939431975, +1.76452265374437994140704763712653054, +1.33377767244509623656120791588648400, +1.80921001213791402542422153177998595, +1.02330358926839205321178192351944991, +1.31433541761240255770435394715121386, +1.11211208940752471513381793434530383, +1.69022561578268554915664505254169947, +1.12390414416232241653593017023629812, +1.08384681300789487406861714103053981, +1.53984869385161699293547738091297681, +1.55182062554704453670899996930373282, +1.29751878644996625640801347000468566, +1.62752180025375483869067537637263790, +1.52433388023688801354622241205248467, +1.50712682125728803656837512368053006, +1.61352787350898883785904041278034509, +1.72330651814793196545325368596084741, +1.09844490017496159053866008891529450, +1.76127118085730280149767460388149284, +1.33099780305757078472435324406403286, +1.75693352037618063651535191489016874, +1.75017614441854658106860734671017908, +1.70038335821838979569144895072663205, +1.51025338516206822085096799523060622, +1.43117672777798507047740154112345204, +1.41181790638817703379207287216457430, +1.03265058958725519106912045872936484, +1.86353387198314515162145229965836682, +1.02021804104142463530150869711733709, +1.40599177460610389902250379586753417, +1.73866167185089708394028143269085740, +1.48037558884174924225423560560785866, +1.60045310366811121682631224626007756, +1.73630636514473538617453278879522336, +1.98410502340028420186579733446208133, +1.95269908463161463921130895608509518, +1.67717668039559364937025518169051635, +1.12642154390708168414980973963331818, +1.97292149545792559725339263370354428

198reltol = sqrt(epsilon(1._TKC))

199reltol

200+0.138777878078144567552953958511352539E-16

201isClose(data, adat, reltol = reltol)

202T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

203call setAsserted(all(isClose(data, adat, reltol = reltol)))

204

205lenData = getUnifRand(5, 100)

206lenData

207+31

208data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

209data

210(+1.43319416, +0.620580971), (+1.15772295, +0.772394955), (+1.18787122, +0.176431000), (+1.45041919, +0.441095173), (+1.24181008, +0.670935452), (+1.46183681, +0.554188490), (+1.83721519, +0.333979905), (+1.80120611, +0.147656858), (+1.75224018, +0.244605899), (+1.62236059, +0.437959194), (+1.89217162, +0.336121261), (+1.78721070, +0.314053893E-1), (+1.79420638, +0.959816575), (+1.68484616, +0.369501114), (+1.48488486, +0.114864886), (+1.61984158, +0.528413236), (+1.12936044, +0.769827485), (+1.02743721, +0.138503671), (+1.73786902, +0.675968170), (+1.19948912, +0.764597833), (+1.57060981, +0.952000618E-1), (+1.12709546, +0.924905837), (+1.33104324, +0.938259959E-1), (+1.68947864, +0.836035013E-1), (+1.82186127, +0.828193069), (+1.07380104, +0.588632226), (+1.74019074, +0.514111698), (+1.32824671, +0.845233202), (+1.98839402, +0.810971856E-1), (+1.19474936, +0.850467741), (+1.12636590, +0.921737313)

211

212adat = getFFTR(getFFTF(data)) / size(data)

213adat

214(+1.43319523, +0.620581210), (+1.15772247, +0.772394955), (+1.18787062, +0.176431015), (+1.45041895, +0.441094995), (+1.24180984, +0.670935333), (+1.46183670, +0.554188371), (+1.83721507, +0.333979696), (+1.80120587, +0.147656724), (+1.75224006, +0.244605824), (+1.62236047, +0.437959164), (+1.89217138, +0.336121172), (+1.78721070, +0.314054526E-1), (+1.79420638, +0.959816515), (+1.68484640, +0.369501173), (+1.48488510, +0.114864871), (+1.61984205, +0.528413355), (+1.12936080, +0.769827545), (+1.02743745, +0.138503626), (+1.73786926, +0.675968289), (+1.19948924, +0.764597654), (+1.57060969, +0.952000916E-1), (+1.12709522, +0.924905896), (+1.33104312, +0.938258767E-1), (+1.68947852, +0.836033821E-1), (+1.82186115, +0.828192949), (+1.07380080, +0.588632107), (+1.74019039, +0.514111578), (+1.32824647, +0.845233083), (+1.98839390, +0.810970813E-1), (+1.19474864, +0.850467682), (+1.12636542, +0.921737313)

215reltol = sqrt(epsilon(1._TKC))

216reltol

217+0.345266977E-3

218isClose(data, adat, reltol = reltol)

219T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

220call setAsserted(all(isClose(data, adat, reltol = reltol)))

221

222lenData = getUnifRand(5, 100)

223lenData

224+92

225data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

226data

227(+1.1499204364327857, +0.10846430705091092), (+1.1453504821405684, +0.51060676590015786E-1), (+1.2324383038834397, +0.68398516717185132), (+1.6646736566385891, +0.93348731387939088E-1), (+1.1585975093430032, +0.56176857527910828), (+1.3832447091384594, +0.27779031297949786E-1), (+1.3829934387838678, +0.49368732468223464), (+1.0038790923235059, +0.97761729775376560E-1), (+1.8880015281161753, +0.23147975545652455), (+1.2038933846825524, +0.82774944974813636E-1), (+1.6014737048516996, +0.39138182187315784), (+1.6458611961083705, +0.93089269969492716), (+1.4490099449858074, +0.97525151246137454), (+1.6714492345423984, +0.30319255763020614), (+1.3649818392222237, +0.14781091709165939), (+1.7981455266727155, +0.87421865633789131), (+1.9668382545159888, +0.51501220655369739), (+1.8671186449339809, +0.32170084842162661E-1), (+1.3308992008903275, +0.17931511265332134), (+1.4052410146413254, +0.85615264049020401), (+1.6481848556407357, +0.23152882067282277), (+1.7473492067028169, +0.99204291236164943), (+1.0102686441408801, +0.93662168932031176), (+1.2536796195617714, +0.13553914226907915), (+1.4193645384034355, +0.14686983822748811), (+1.6218249674149905, +0.75170643796485626), (+1.0142999930731202, +0.19684664301383703), (+1.6652126391541429, +0.73681897378707562E-1), (+1.8973845341902122, +0.64730622835867691), (+1.9352476099290463, +0.70633267295695312), (+1.4138618902522166, +0.61324317097216541), (+1.2363169497133100, +0.69901775994409054), (+1.8022794592560296, +0.18762628852161811), (+1.1692556574707615, +0.69713170324348883), (+1.0201836634552073, +0.16876260206029015), (+1.3444841500944456, +0.75594007298789445), (+1.5721525804648624, +0.39977032051967487), (+1.4436613118196229, +0.34917576553521057), (+1.0606969183212542, +0.12220346853037334), (+1.8892099763502630, +0.92441553083538597), (+1.2351025410794729, +0.39148534312103078), (+1.2262590109077673, +0.97679368569872937), (+1.7406232479568551, +0.19799676584217052), (+1.8506486268193982, +0.78669269968943933), (+1.9645754939735378, +0.54077696680998288), (+1.7754732747480946, +0.17997005990337400), (+1.4689320437509665, +0.44354941753425836), (+1.9388866928280901, +0.64727624670806760), (+1.2627426569415210, +0.70414397501661652), (+1.9837476934661056, +0.33595372515902611E-1), (+1.4565533726328390, +0.69760082734076156), (+1.1938766233726110, +0.97904626306646869E-1), (+1.0480475394469999, +0.27265343633787087), (+1.1891448697285483, +0.34076421316468597), (+1.1235415463303167, +0.36561915966096137), (+1.2450917845155507, +0.34840952105556777), (+1.2576275282778973, +0.87049404474747061), (+1.2930489303438968, +0.55885055611130352), (+1.4012924872544890, +0.96397551753420019E-1), (+1.9505151492925195, +0.28625054090962754), (+1.1993530641404511, +0.10847650455104485), (+1.4507691033291992, +0.80364012778463734), (+1.1979810534034387, +0.42518225472469384), (+1.3238636778170811, +0.16966645340091624E-1), (+1.1549968242253192, +0.98388740005622244), (+1.3556572620616230, +0.99493606117163524), (+1.5480024720989896, +0.15971304663706076), (+1.0856538476697295, +0.73056971559782491), (+1.3060125956191424, +0.40834077498592025), (+1.3252089652893795, +0.85731939675085411), (+1.6695787456245967, +0.25639403037912389), (+1.2197798359505247, +0.85463224315350717), (+1.4831356019330029, +0.10796573759086414), (+1.0186992243146404, +0.62127761727464370), (+1.1300150096723900, +0.72112044194060365E-2), (+1.8589663032461230, +0.45792873759208697), (+1.8573198911406967, +0.80619852178279938E-1), (+1.8552530865166459, +0.88136726925879372E-1), (+1.6383149545799445, +0.82745546105022050), (+1.3975028709758361, +0.79523075882562022), (+1.7239277869960479, +0.31782356395724987), (+1.2628609287050225, +0.43722506901880021), (+1.4358956595872483, +0.92218597332430985E-1), (+1.2501399601667655, +0.42748690408725132), (+1.9232502496323616, +0.68447963434906733), (+1.2292430776900436, +0.19485161839000020), (+1.2993493821219850, +0.25484589729134710), (+1.7725076361110057, +0.93456805409744881), (+1.7217065130401024, +0.80991395233714558), (+1.0840360596120640, +0.11547023577101567), (+1.4442747538371161, +0.69098178880984229), (+1.4438784407805543, +0.75461178681013330)

228

229adat = getFFTR(getFFTF(data)) / size(data)

230adat

231(+1.1499204364327835, +0.10846430705091005), (+1.1453504821405693, +0.51060676590016098E-1), (+1.2324383038834399, +0.68398516717185143), (+1.6646736566385893, +0.93348731387938810E-1), (+1.1585975093430030, +0.56176857527910828), (+1.3832447091384594, +0.27779031297949553E-1), (+1.3829934387838683, +0.49368732468223481), (+1.0038790923235061, +0.97761729775376574E-1), (+1.8880015281161753, +0.23147975545652458), (+1.2038933846825521, +0.82774944974813400E-1), (+1.6014737048516998, +0.39138182187315801), (+1.6458611961083691, +0.93089269969492672), (+1.4490099449858067, +0.97525151246137409), (+1.6714492345423984, +0.30319255763020631), (+1.3649818392222237, +0.14781091709165925), (+1.7981455266727158, +0.87421865633789153), (+1.9668382545159886, +0.51501220655369750), (+1.8671186449339807, +0.32170084842162598E-1), (+1.3308992008903275, +0.17931511265332106), (+1.4052410146413257, +0.85615264049020423), (+1.6481848556407359, +0.23152882067282307), (+1.7473492067028171, +0.99204291236164932), (+1.0102686441408808, +0.93662168932031231), (+1.2536796195617688, +0.13553914226907829), (+1.4193645384034361, +0.14686983822748861), (+1.6218249674149907, +0.75170643796485637), (+1.0142999930731198, +0.19684664301383692), (+1.6652126391541433, +0.73681897378707548E-1), (+1.8973845341902129, +0.64730622835867702), (+1.9352476099290465, +0.70633267295695301), (+1.4138618902522164, +0.61324317097216519), (+1.2363169497133106, +0.69901775994409077), (+1.8022794592560298, +0.18762628852161836), (+1.1692556574707618, +0.69713170324348883), (+1.0201836634552064, +0.16876260206028973), (+1.3444841500944449, +0.75594007298789412), (+1.5721525804648631, +0.39977032051967498), (+1.4436613118196233, +0.34917576553521057), (+1.0606969183212538, +0.12220346853037310), (+1.8892099763502626, +0.92441553083538608), (+1.2351025410794738, +0.39148534312103073), (+1.2262590109077673, +0.97679368569872960), (+1.7406232479568551, +0.19799676584217049), (+1.8506486268193980, +0.78669269968943956), (+1.9645754939735387, +0.54077696680998311), (+1.7754732747480950, +0.17997005990337445), (+1.4689320437509648, +0.44354941753425747), (+1.9388866928280910, +0.64727624670806827), (+1.2627426569415214, +0.70414397501661652), (+1.9837476934661054, +0.33595372515902611E-1), (+1.4565533726328390, +0.69760082734076123), (+1.1938766233726106, +0.97904626306646772E-1), (+1.0480475394470004, +0.27265343633787126), (+1.1891448697285483, +0.34076421316468614), (+1.1235415463303164, +0.36561915966096131), (+1.2450917845155509, +0.34840952105556788), (+1.2576275282778975, +0.87049404474747083), (+1.2930489303438963, +0.55885055611130330), (+1.4012924872544879, +0.96397551753419616E-1), (+1.9505151492925195, +0.28625054090962765), (+1.1993530641404513, +0.10847650455104485), (+1.4507691033291996, +0.80364012778463734), (+1.1979810534034387, +0.42518225472469373), (+1.3238636778170814, +0.16966645340091818E-1), (+1.1549968242253197, +0.98388740005622211), (+1.3556572620616232, +0.99493606117163513), (+1.5480024720989893, +0.15971304663706073), (+1.0856538476697304, +0.73056971559782535), (+1.3060125956191433, +0.40834077498592075), (+1.3252089652893773, +0.85731939675085345), (+1.6695787456245967, +0.25639403037912417), (+1.2197798359505256, +0.85463224315350739), (+1.4831356019330031, +0.10796573759086427), (+1.0186992243146402, +0.62127761727464370), (+1.1300150096723902, +0.72112044194061666E-2), (+1.8589663032461232, +0.45792873759208730), (+1.8573198911406970, +0.80619852178279799E-1), (+1.8552530865166452, +0.88136726925879427E-1), (+1.6383149545799440, +0.82745546105022061), (+1.3975028709758370, +0.79523075882562000), (+1.7239277869960474, +0.31782356395724970), (+1.2628609287050214, +0.43722506901879971), (+1.4358956595872481, +0.92218597332430693E-1), (+1.2501399601667658, +0.42748690408725137), (+1.9232502496323614, +0.68447963434906722), (+1.2292430776900436, +0.19485161838999990), (+1.2993493821219850, +0.25484589729134682), (+1.7725076361110055, +0.93456805409744903), (+1.7217065130401024, +0.80991395233714580), (+1.0840360596120637, +0.11547023577101569), (+1.4442747538371168, +0.69098178880984218), (+1.4438784407805554, +0.75461178681013341)

232reltol = sqrt(epsilon(1._TKC))

233reltol

234+0.14901161193847656E-7

235isClose(data, adat, reltol = reltol)

236T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

237call setAsserted(all(isClose(data, adat, reltol = reltol)))

238

239lenData = getUnifRand(5, 100)

240lenData

241+8

242data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

243data

244(+1.38023347590248185780964136639180267, +0.933827631561704816800813787182272186), (+1.96735954417595015807946220485435029, +0.347363883056474702402903838493144282), (+1.70486210073616817045103165385920858, +0.144805127051359446703714116971389437), (+1.43196654659032247194295079914107608, +0.707679991843556783811029810929177766E-1), (+1.36883789306499510628781222486692253, +0.500896198956996637856515472033179681), (+1.58253058462258452534662945633063199, +0.671566376289118400108632154976975085), (+1.26558032488799723870879909180390860, +0.968583593563919646286653075182646183E-1), (+1.80346025785176903145093933996872708, +0.488644128469263885486661969252154314)

245

246adat = getFFTR(getFFTF(data)) / size(data)

247adat

248(+1.38023347590248185780964136639180267, +0.933827631561704816800813787182272186), (+1.96735954417595015807946220485435029, +0.347363883056474702402903838493144282), (+1.70486210073616817045103165385920858, +0.144805127051359446703714116971389413), (+1.43196654659032247194295079914107608, +0.707679991843556783811029810929178007E-1), (+1.36883789306499510628781222486692253, +0.500896198956996637856515472033179778), (+1.58253058462258452534662945633063199, +0.671566376289118400108632154976974989), (+1.26558032488799723870879909180390860, +0.968583593563919646286653075182645461E-1), (+1.80346025785176903145093933996872689, +0.488644128469263885486661969252154314)

249reltol = sqrt(epsilon(1._TKC))

250reltol

251+0.138777878078144567552953958511352539E-16

252isClose(data, adat, reltol = reltol)

253T, T, T, T, T, T, T, T

254call setAsserted(all(isClose(data, adat, reltol = reltol)))

255

256lenData = getUnifRand(5, 100)

257lenData

258+18

259data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

260data

261+1.30865812, +1.62783384, +1.72613144, +1.92311645, +1.44670892, +1.96882951, +1.44054818, +1.65584159, +1.09209561, +1.16832089, +1.36437488, +1.85411024, +1.45805323, +1.59999084, +1.73840642, +1.86054230, +1.70757484, +1.06647766

262

263adat = getFFTR(getFFTF(data)) / size(data)

264adat

265+1.30865812, +1.62783372, +1.72613156, +1.92311645, +1.44670916, +1.96882951, +1.44054830, +1.65584147, +1.09209585, +1.16832101, +1.36437511, +1.85411024, +1.45805323, +1.59999073, +1.73840666, +1.86054230, +1.70757496, +1.06647778

266reltol = sqrt(epsilon(1._TKC))

267reltol

268+0.345266977E-3

269isClose(data, adat, reltol = reltol)

270T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

271call setAsserted(all(isClose(data, adat, reltol = reltol)))

272

273lenData = getUnifRand(5, 100)

274lenData

275+89

276data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

277data

278+1.1137724913152938, +1.9994914998394491, +1.9632197922425934, +1.7853658545465738, +1.8425884740033025, +1.7172261424760316, +1.7666901503428938, +1.8174889299473067, +1.0048325622577980, +1.0680585908093041, +1.6787768784971826, +1.5821527203659742, +1.6730817851604227, +1.9808097643178402, +1.7781431185272167, +1.3572460315477779, +1.0706844771809678, +1.1467110705590979, +1.3307488118392881, +1.8175282905249757, +1.6023467661835673, +1.2067224464779236, +1.3111123077303395, +1.3552095696789661, +1.7119699127423917, +1.0995870195509463, +1.1862241165641909, +1.4589049898404935, +1.5806413339366363, +1.9604727909620305, +1.1776039897563200, +1.6182403937056300, +1.7564263185037066, +1.2420909016939063, +1.3212403247090410, +1.5458811062968874, +1.0361263476027178, +1.6973824257926688, +1.8814787177352787, +1.3901699924589650, +1.3553124090933135, +1.1285357461438914, +1.7335418277003281, +1.1446782331420147, +1.8272466921622459, +1.7275992332245504, +1.7146700793970857, +1.0668506187409903, +1.4583859018449123, +1.5757308349176355, +1.4997215453385979, +1.8439657757630532, +1.0336905817307802, +1.9818192474332430, +1.2085190020376859, +1.2953149232283609, +1.6199522118408187, +1.5611741015565777, +1.9775708983543445, +1.3608572525487168, +1.1743214817998464, +1.0776859187667793, +1.8730434064380652, +1.2361069510923488, +1.9579275001817775, +1.1576694265506673, +1.9531270510434293, +1.7964898316434454, +1.9094447350390733, +1.6765327005057045, +1.0775089617879647, +1.5701366292081760, +1.4424949837498864, +1.9462510441565335, +1.8595863302967750, +1.8186626429148114, +1.8991354276441579, +1.8811827614331706, +1.1635984840836295, +1.5683026319692921, +1.7327036253707355, +1.5523267207685238, +1.7371220225429238, +1.9116337229422307, +1.2114204315675505, +1.2258997451296305, +1.1453514730827661, +1.6714813132741133, +1.0645625083400088

279

280adat = getFFTR(getFFTF(data)) / size(data)

281adat

282+1.1137724913152962, +1.9994914998394515, +1.9632197922425931, +1.7853658545465765, +1.8425884740033032, +1.7172261424760340, +1.7666901503428940, +1.8174889299473016, +1.0048325622578060, +1.0680585908093123, +1.6787768784971795, +1.5821527203659771, +1.6730817851604227, +1.9808097643178324, +1.7781431185272125, +1.3572460315477806, +1.0706844771809743, +1.1467110705591017, +1.3307488118392925, +1.8175282905249637, +1.6023467661835631, +1.2067224464779329, +1.3111123077303413, +1.3552095696789721, +1.7119699127423726, +1.0995870195509625, +1.1862241165641969, +1.4589049898404913, +1.5806413339366374, +1.9604727909620012, +1.1776039897563464, +1.6182403937056198, +1.7564263185036881, +1.2420909016939199, +1.3212403247090472, +1.5458811062968687, +1.0361263476027507, +1.6973824257926553, +1.8814787177352517, +1.3901699924589750, +1.3553124090933084, +1.1285357461439238, +1.7335418277002939, +1.1446782331420657, +1.8272466921622017, +1.7275992332245309, +1.7146700793970748, +1.0668506187410289, +1.4583859018449075, +1.5757308349176262, +1.4997215453386079, +1.8439657757630170, +1.0336905817308297, +1.9818192474331935, +1.2085190020377106, +1.2953149232283689, +1.6199522118408056, +1.5611741015565852, +1.9775708983543141, +1.3608572525487292, +1.1743214817998509, +1.0776859187668024, +1.8730434064380328, +1.2361069510923777, +1.9579275001817487, +1.1576694265506970, +1.9531270510434129, +1.7964898316434446, +1.9094447350390678, +1.6765327005056951, +1.0775089617879841, +1.5701366292081684, +1.4424949837498957, +1.9462510441565228, +1.8595863302967748, +1.8186626429148094, +1.8991354276441561, +1.8811827614331640, +1.1635984840836417, +1.5683026319692916, +1.7327036253707346, +1.5523267207685276, +1.7371220225429251, +1.9116337229422267, +1.2114204315675576, +1.2258997451296323, +1.1453514730827707, +1.6714813132741122, +1.0645625083400123

283reltol = sqrt(epsilon(1._TKC))

284reltol

285+0.14901161193847656E-7

286isClose(data, adat, reltol = reltol)

287T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

288call setAsserted(all(isClose(data, adat, reltol = reltol)))

289

290lenData = getUnifRand(5, 100)

291lenData

292+40

293data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

294data

295+1.81342635483709685734780267769946989, +1.25236317305015523049423007560766058, +1.48307273797234676971720346598157247, +1.74277601545373691096675487226354395, +1.57933541314211199240725504195158242, +1.60553639494092204694814554937548319, +1.18758291742450824864997024515589786, +1.38581059940578802880854958072211253, +1.44053680524513159961085532857672674, +1.96530285521395999391038207136458767, +1.94483866814241907848323621285682067, +1.22378686190078389548951653895178456, +1.26418014669612230678866332361449114, +1.33223126436075332687528013922409679, +1.57142154639976780019970168636416262, +1.36111577231306427904673066122811893, +1.38530118363958167460190403224124818, +1.83953880277311160588575482818843927, +1.64918969438066388769038553648379488, +1.51922867902090061270358017663688159, +1.18719218088029747556215808725585003, +1.93002178807919356443809511177365819, +1.88420687448243536736469889812681572, +1.44505221115917070358927356358605790, +1.73582778782959456571922258751398542, +1.91965293266320706225905494692619881, +1.95259300696962106164939755244346040, +1.24789186605911750169842486217392925, +1.87147704095752928309120340072809077, +1.94184781270558647190029440361133735, +1.62625151606158740573494475737968000, +1.89105402762059644367096553708279952, +1.38803896210245585980928247640413516, +1.26276284801260739361642151514978089, +1.17583674389406289208187727629231424, +1.95780468926630126937933007102623722, +1.29828907631933306801148707952368340, +1.25388060752289799696282910653825672, +1.16723136601265716807822227509937012, +1.12279292306259402968499721151514322

296

297adat = getFFTR(getFFTF(data)) / size(data)

298adat

299+1.81342635483709685734780267769946969, +1.25236317305015523049423007560766058, +1.48307273797234676971720346598157208, +1.74277601545373691096675487226354375, +1.57933541314211199240725504195158242, +1.60553639494092204694814554937548300, +1.18758291742450824864997024515589767, +1.38581059940578802880854958072211253, +1.44053680524513159961085532857672674, +1.96530285521395999391038207136458748, +1.94483866814241907848323621285682067, +1.22378686190078389548951653895178456, +1.26418014669612230678866332361449152, +1.33223126436075332687528013922409679, +1.57142154639976780019970168636416243, +1.36111577231306427904673066122811913, +1.38530118363958167460190403224124799, +1.83953880277311160588575482818843927, +1.64918969438066388769038553648379488, +1.51922867902090061270358017663688159, +1.18719218088029747556215808725585023, +1.93002178807919356443809511177365838, +1.88420687448243536736469889812681591, +1.44505221115917070358927356358605809, +1.73582778782959456571922258751398523, +1.91965293266320706225905494692619881, +1.95259300696962106164939755244346001, +1.24789186605911750169842486217392964, +1.87147704095752928309120340072809077, +1.94184781270558647190029440361133735, +1.62625151606158740573494475737968000, +1.89105402762059644367096553708279952, +1.38803896210245585980928247640413516, +1.26276284801260739361642151514978089, +1.17583674389406289208187727629231424, +1.95780468926630126937933007102623722, +1.29828907631933306801148707952368378, +1.25388060752289799696282910653825672, +1.16723136601265716807822227509936993, +1.12279292306259402968499721151514360

300reltol = sqrt(epsilon(1._TKC))

301reltol

302+0.138777878078144567552953958511352539E-16

303isClose(data, adat, reltol = reltol)

304T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

305call setAsserted(all(isClose(data, adat, reltol = reltol)))

306

307lenData = getUnifRand(5, 100)

308lenData

309+36

310data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

311data

312(+1.00488150, +0.927872002), (+1.01171517, +0.722633779), (+1.97437370, +0.253263652), (+1.49749053, +0.473660409), (+1.55576777, +0.322309136E-1), (+1.96677840, +0.738547027), (+1.03642344, +0.122398674), (+1.46608233, +0.333628178), (+1.72586906, +0.953185439), (+1.49098635, +0.172214508E-1), (+1.25021827, +0.630690634), (+1.82922399, +0.439075232E-1), (+1.11603796, +0.462277412), (+1.93034172, +0.480299532), (+1.73761630, +0.303304017), (+1.24676156, +0.753165245), (+1.32825601, +0.799825668), (+1.92963040, +0.136342406), (+1.87702668, +0.361105204), (+1.17823219, +0.481052876), (+1.14995897, +0.793044209), (+1.11604309, +0.429596245), (+1.31164241, +0.891475558), (+1.08745265, +0.122618139), (+1.94778335, +0.908845365), (+1.63258100, +0.885427952), (+1.73234010, +0.664408326), (+1.79499531, +0.110334218), (+1.73983979, +0.739300430), (+1.82843304, +0.653418243), (+1.19380522, +0.234320223), (+1.62789810, +0.701967478E-1), (+1.75453496, +0.690776050), (+1.37189627, +0.117636383), (+1.64383543, +0.114417732), (+1.06097615, +0.934848905)

313

314adat = getFFTR(getFFTF(data)) / size(data)

315adat

316(+1.00488150, +0.927872002), (+1.01171541, +0.722633779), (+1.97437370, +0.253263623), (+1.49749064, +0.473660409), (+1.55576789, +0.322309881E-1), (+1.96677840, +0.738546908), (+1.03642333, +0.122398645), (+1.46608257, +0.333628088), (+1.72586918, +0.953185380), (+1.49098647, +0.172213707E-1), (+1.25021851, +0.630690634), (+1.82922411, +0.439073779E-1), (+1.11603808, +0.462277472), (+1.93034196, +0.480299532), (+1.73761630, +0.303303987), (+1.24676156, +0.753165126), (+1.32825601, +0.799825668), (+1.92963052, +0.136342391), (+1.87702644, +0.361105084), (+1.17823267, +0.481052816), (+1.14995909, +0.793044150), (+1.11604321, +0.429596215), (+1.31164253, +0.891475439), (+1.08745277, +0.122618094), (+1.94778335, +0.908845484), (+1.63258100, +0.885427892), (+1.73234022, +0.664408207), (+1.79499543, +0.110334210), (+1.73983979, +0.739300489), (+1.82843316, +0.653418124), (+1.19380522, +0.234320164), (+1.62789834, +0.701967180E-1), (+1.75453496, +0.690776050), (+1.37189627, +0.117636338), (+1.64383554, +0.114417605), (+1.06097627, +0.934848666)

317reltol = sqrt(epsilon(1._TKC))

318reltol

319+0.345266977E-3

320isClose(data, adat, reltol = reltol)

321T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

322call setAsserted(all(isClose(data, adat, reltol = reltol)))

323

324lenData = getUnifRand(5, 100)

325lenData

326+16

327data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

328data

329(+1.8166088809991483, +0.45161944288280897), (+1.1371364627247345, +0.21031013830696321), (+1.0603601776431901, +0.32482523321152978), (+1.0044962494121479, +0.15395127224647531), (+1.8456926898865229, +0.99525917897296046), (+1.8672605269580562, +0.90040464385222174E-1), (+1.5416731217099890, +0.20309481496282866E-1), (+1.9622233387523509, +0.49077844917837332), (+1.2988355450949094, +0.69684597522014857), (+1.2741054601799995, +0.61077603521304225), (+1.3145084918692014, +0.67125943369642871), (+1.3456122087155333, +0.80618160395857663), (+1.1362051084564002, +0.99034770460167953), (+1.6846032413178218, +0.75249721231099453), (+1.2857597793583473, +0.65522364262830846), (+1.6051013383618660, +0.63888698602828831)

330

331adat = getFFTR(getFFTF(data)) / size(data)

332adat

333(+1.8166088809991483, +0.45161944288280892), (+1.1371364627247342, +0.21031013830696324), (+1.0603601776431901, +0.32482523321152984), (+1.0044962494121479, +0.15395127224647531), (+1.8456926898865227, +0.99525917897296035), (+1.8672605269580560, +0.90040464385222063E-1), (+1.5416731217099890, +0.20309481496282977E-1), (+1.9622233387523507, +0.49077844917837327), (+1.2988355450949092, +0.69684597522014846), (+1.2741054601799993, +0.61077603521304225), (+1.3145084918692014, +0.67125943369642882), (+1.3456122087155333, +0.80618160395857652), (+1.1362051084564002, +0.99034770460167953), (+1.6846032413178216, +0.75249721231099442), (+1.2857597793583473, +0.65522364262830846), (+1.6051013383618657, +0.63888698602828820)

334reltol = sqrt(epsilon(1._TKC))

335reltol

336+0.14901161193847656E-7

337isClose(data, adat, reltol = reltol)

338T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

339call setAsserted(all(isClose(data, adat, reltol = reltol)))

340

341lenData = getUnifRand(5, 100)

342lenData

343+85

344data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

345data

346(+1.23272414036705298305241567904185792, +0.251305719934177231231840100761715715), (+1.75857542567828852345073929125874527, +0.830050141714691359619577773241235775), (+1.60146214121886078235822040035583614, +0.215201194709414605458589285058199334), (+1.86630364429341316096423471281230483, +0.136358126839344701122742539819906818), (+1.64151727292253535008194773132323645, +0.186615021156303125410962687583989143), (+1.60923193782678045348986878203537364, +0.963098676039958885981472668367044646), (+1.55156856979020621949191930815389960, +0.631743382158155494657832041916355553), (+1.05173299285823907229845000279744718, +0.780108882392892767266938305958083984), (+1.85403022190056283348377507204822610, +0.876912462843587412047849790675788808), (+1.01983787078905904210564192621000273, +0.475257947271723090459680616886303816), (+1.20439080122382964832882877025647027, +0.835015285020364974627872937609657699), (+1.89498843358007203570037053728586941, +0.332608230305228581621673150253261502), 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347

348adat = getFFTR(getFFTF(data)) / size(data)

349adat

350(+1.23272414036705298305241567904185792, +0.251305719934177231231840100761715523), (+1.75857542567828852345073929125874527, +0.830050141714691359619577773241235679), (+1.60146214121886078235822040035583557, +0.215201194709414605458589285058199069), (+1.86630364429341316096423471281230406, +0.136358126839344701122742539819906408), (+1.64151727292253535008194773132323626, +0.186615021156303125410962687583988974), (+1.60923193782678045348986878203537364, +0.963098676039958885981472668367044646), (+1.55156856979020621949191930815389980, +0.631743382158155494657832041916355457), (+1.05173299285823907229845000279744660, +0.780108882392892767266938305958083791), (+1.85403022190056283348377507204822590, +0.876912462843587412047849790675788808), (+1.01983787078905904210564192621000254, +0.475257947271723090459680616886303864), (+1.20439080122382964832882877025646988, +0.835015285020364974627872937609657603), (+1.89498843358007203570037053728586980, +0.332608230305228581621673150253261406), 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+0.157551738779643673147218812384854932), (+1.53866306467131606434395533076381390, +0.411531225168659507363233902423556101)

351reltol = sqrt(epsilon(1._TKC))

352reltol

353+0.138777878078144567552953958511352539E-16

354isClose(data, adat, reltol = reltol)

355T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

356call setAsserted(all(isClose(data, adat, reltol = reltol)))

357

358lenData = getUnifRand(5, 100)

359lenData

360+20

361data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

362data

363+1.12149024, +1.89287710, +1.13922441, +1.62978673, +1.22995281, +1.96718645, +1.33442855, +1.10824585, +1.83361804, +1.08686185, +1.55072534, +1.11262298, +1.69843113, +1.52158594, +1.14959455, +1.67043483, +1.28635502, +1.72380602, +1.39392400, +1.46727610

364

365adat = getFFTR(getFFTF(data)) / size(data)

366adat

367+1.12148976, +1.89287686, +1.13922405, +1.62978649, +1.22995281, +1.96718633, +1.33442855, +1.10824597, +1.83361816, +1.08686185, +1.55072534, +1.11262298, +1.69843137, +1.52158582, +1.14959455, +1.67043471, +1.28635502, +1.72380602, +1.39392388, +1.46727610

368reltol = sqrt(epsilon(1._TKC))

369reltol

370+0.345266977E-3

371isClose(data, adat, reltol = reltol)

372T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

373call setAsserted(all(isClose(data, adat, reltol = reltol)))

374

375lenData = getUnifRand(5, 100)

376lenData

377+51

378data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

379data

380+1.9132188789798257, +1.5521613514137460, +1.3314152138436535, +1.1967904316225944, +1.3546628521396014, +1.8783436459963361, +1.9926530826031037, +1.9526916613900513, +1.8140922797424097, +1.2199872306473183, +1.5794987646836463, +1.6921917415362313, +1.9932855830019509, +1.9777566361702568, +1.3245899120082698, +1.0730825970395101, +1.5402657740691152, +1.6699037870123290, +1.6485816045791215, +1.5473272681893788, +1.5350781267925497, +1.9317845651605001, +1.9350508177972205, +1.0216685885872208, +1.2166182900802500, +1.7110707195519095, +1.0028965628950717, +1.2401615085112865, +1.8099967990021590, +1.8009304465977911, +1.8328071112706841, +1.8604110218350716, +1.1552706414552665, +1.6834235158868935, +1.1828036904976118, +1.1521579103658803, +1.5004510607128105, +1.7408741271319219, +1.3287512626499012, +1.4304034959348733, +1.1709732026806432, +1.1109421385252305, +1.0987198010136769, +1.2263670892309420, +1.6248909592855858, +1.8294097405376519, +1.5456217195866901, +1.9626304776786569, +1.7213540647293131, +1.2939872044531109, +1.1913972889176454

381

382adat = getFFTR(getFFTF(data)) / size(data)

383adat

384+1.9132188789798255, +1.5521613514137462, +1.3314152138436537, +1.1967904316225948, +1.3546628521396020, +1.8783436459963370, +1.9926530826031035, +1.9526916613900516, +1.8140922797424099, +1.2199872306473190, +1.5794987646836460, +1.6921917415362322, +1.9932855830019502, +1.9777566361702568, +1.3245899120082698, +1.0730825970395095, +1.5402657740691150, +1.6699037870123297, +1.6485816045791211, +1.5473272681893784, +1.5350781267925493, +1.9317845651605012, +1.9350508177972217, +1.0216685885872216, +1.2166182900802496, +1.7110707195519095, +1.0028965628950708, +1.2401615085112860, +1.8099967990021586, +1.8009304465977904, +1.8328071112706854, +1.8604110218350727, +1.1552706414552669, +1.6834235158868929, +1.1828036904976114, +1.1521579103658792, +1.5004510607128099, +1.7408741271319217, +1.3287512626499014, +1.4304034959348726, +1.1709732026806430, +1.1109421385252305, +1.0987198010136776, +1.2263670892309417, +1.6248909592855865, +1.8294097405376517, +1.5456217195866904, +1.9626304776786574, +1.7213540647293135, +1.2939872044531118, +1.1913972889176461

385reltol = sqrt(epsilon(1._TKC))

386reltol

387+0.14901161193847656E-7

388isClose(data, adat, reltol = reltol)

389T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

390call setAsserted(all(isClose(data, adat, reltol = reltol)))

391

392lenData = getUnifRand(5, 100)

393lenData

394+32

395data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

396data

397+1.95005493531716575927379265074900583, +1.96273580008542664822303393863403896, +1.38620677324802040504504041721352038, +1.21768115638530141794111375918745600, +1.06940643294614358842659200328399938, +1.42959940822478889376169306442496603, +1.70933604716805757551805503864054537, +1.32348749838148794973803847864996099, +1.01528181699797905554600127462280465, +1.14489772176718313466441734090384835, +1.42637204676115718848578952985211603, +1.48703022360952254886238153994347065, +1.19803612582885513077558139479043232, +1.48440346375398447355065836009504603, +1.89351116627612393427619701730601688, +1.38361743417829876281025752457368474, +1.80338013059944662823757573508079953, +1.28586942159690020272778329945935632, +1.30348522705198380895394483297188547, +1.29805742688047448152545196504555245, +1.90124011427144468981510396630036574, +1.01375622382983952091222261889424769, +1.94665067092340806247511318198198759, +1.80758253382615095988958903421713313, +1.57758059234594995793441850020228332, +1.65628207106539037477839411377178556, +1.62701578692328812888176232501122580, +1.17013457737328193565376356678074714, +1.15612451154579372305043256943311198, +1.77589018611556900243056856873872991, +1.39845645119779415275718084772790300, +1.20898547906287305355164367487385600

398

399adat = getFFTR(getFFTF(data)) / size(data)

400adat

401+1.95005493531716575927379265074900583, +1.96273580008542664822303393863403896, +1.38620677324802040504504041721352038, +1.21768115638530141794111375918745600, +1.06940643294614358842659200328399938, +1.42959940822478889376169306442496622, +1.70933604716805757551805503864054518, +1.32348749838148794973803847864996080, +1.01528181699797905554600127462280446, +1.14489772176718313466441734090384854, +1.42637204676115718848578952985211584, +1.48703022360952254886238153994347084, +1.19803612582885513077558139479043232, +1.48440346375398447355065836009504622, +1.89351116627612393427619701730601688, +1.38361743417829876281025752457368455, +1.80338013059944662823757573508079953, +1.28586942159690020272778329945935632, +1.30348522705198380895394483297188547, +1.29805742688047448152545196504555264, +1.90124011427144468981510396630036574, +1.01375622382983952091222261889424769, +1.94665067092340806247511318198198740, +1.80758253382615095988958903421713294, +1.57758059234594995793441850020228332, +1.65628207106539037477839411377178556, +1.62701578692328812888176232501122561, +1.17013457737328193565376356678074733, +1.15612451154579372305043256943311198, +1.77589018611556900243056856873873010, +1.39845645119779415275718084772790300, +1.20898547906287305355164367487385600

402reltol = sqrt(epsilon(1._TKC))

403reltol

404+0.138777878078144567552953958511352539E-16

405isClose(data, adat, reltol = reltol)

406T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

407call setAsserted(all(isClose(data, adat, reltol = reltol)))

408

409lenData = getUnifRand(5, 100)

410lenData

411+38

412data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

413data

414(+1.22927976, +0.521759033), (+1.25318432, +0.549354494), (+1.57924652, +0.196349621E-2), (+1.64753509, +0.332803309), (+1.80112553, +0.146002531), (+1.61872482, +0.574895024), (+1.41089559, +0.654422045E-1), (+1.51014364, +0.171121418), (+1.49364471, +0.234032929), (+1.53977060, +0.696775794), (+1.65911829, +0.770344198), (+1.10381448, +0.846586645), (+1.20447087, +0.265482008), (+1.41490018, +0.401026011), (+1.78309512, +0.510396779), (+1.79047132, +0.889528513), (+1.76873410, +0.540845037), (+1.18717432, +0.180993438), (+1.73809195, +0.104119003), (+1.70276618, +0.158864558), (+1.06637478, +0.515364349), (+1.16561413, +0.401785195), (+1.29796302, +0.383557677E-1), (+1.72208810, +0.608136714), (+1.32329834, +0.416668832), (+1.09970880, +0.595248699), (+1.85590148, +0.926989675), (+1.35623789, +0.446312249), (+1.65707445, +0.209150314E-1), (+1.28409386, +0.612557948), (+1.75954580, +0.106508851), (+1.95518064, +0.106017590), (+1.74725461, +0.460969269), (+1.72340333, +0.775101781E-1), (+1.39501047, +0.502638340), (+1.64184999, +0.904956639), (+1.10016537, +0.732649386), (+1.99066520, +0.761147678)

415

416adat = getFFTR(getFFTF(data)) / size(data)

417adat

418(+1.22927940, +0.521759033), (+1.25318432, +0.549354494), (+1.57924640, +0.196346478E-2), (+1.64753497, +0.332803339), (+1.80112541, +0.146002606), (+1.61872482, +0.574895084), (+1.41089547, +0.654422641E-1), (+1.51014328, +0.171121314), (+1.49364448, +0.234032854), (+1.53977084, +0.696775913), (+1.65911829, +0.770344198), (+1.10381436, +0.846586645), (+1.20447063, +0.265481979), (+1.41490006, +0.401026070), (+1.78309512, +0.510396779), (+1.79047132, +0.889528573), (+1.76873422, +0.540845096), (+1.18717420, +0.180993482), (+1.73809171, +0.104118921), (+1.70276606, +0.158864394), (+1.06637454, +0.515364408), (+1.16561413, +0.401785016), (+1.29796302, +0.383557007E-1), (+1.72208810, +0.608136654), (+1.32329834, +0.416668832), (+1.09970891, +0.595248759), (+1.85590124, +0.926989734), (+1.35623765, +0.446312159), (+1.65707469, +0.209150072E-1), (+1.28409398, +0.612558067), (+1.75954556, +0.106508829), (+1.95518053, +0.106017567), (+1.74725437, +0.460969329), (+1.72340310, +0.775102526E-1), (+1.39501035, +0.502638280), (+1.64185011, +0.904956698), (+1.10016525, +0.732649386), (+1.99066508, +0.761147678)

419reltol = sqrt(epsilon(1._TKC))

420reltol

421+0.345266977E-3

422isClose(data, adat, reltol = reltol)

423T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

424call setAsserted(all(isClose(data, adat, reltol = reltol)))

425

426lenData = getUnifRand(5, 100)

427lenData

428+35

429data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

430data

431(+1.3968930089553426, +0.85170565312914326), (+1.6393241430302599, +0.16058717404769374), (+1.2283514245856857, +0.39822636799664468), (+1.0217494212957092, +0.76089594690443796), (+1.2573921365976157, +0.65084800793290831), (+1.9904319771633834, +0.26093487331342224), (+1.8586582243997500, +0.42831635476098373), (+1.9521141668157145, +0.11954994784959738), (+1.1223615425027391, +0.61663267257183185), (+1.0683963185925192, +0.23541024655030029), (+1.7377975334534765, +0.77609919417268081), (+1.8721491458397610, +0.19729690070511596), (+1.6868431135230260, +0.66130649422446375), (+1.5387331419885744, +0.68489747458973183), (+1.9422204998800461, +0.18010749457763375E-1), (+1.5866304534295002, +0.36652847035100145), (+1.1631441455091858, +0.54703632715029127), (+1.0666563423860831, +0.85006479642421895), (+1.2050783399556240, +0.10115655975689652), (+1.7649487959078585, +0.87325714455776415), (+1.8985253437218050, +0.71413227003353963), (+1.4581035526750059, +0.19606362797248456), (+1.6013346943460369, +0.58170479837877009), (+1.6600930256592181, +0.76669906916998631), (+1.0687537282538049, +0.64113254262316588), (+1.3145922729417268, +0.70303195200922719), (+1.8364503609075471, +0.61355309151825244), (+1.8129613224977423, +0.12783849962164318), (+1.2357781766821700, +0.41177964123227995), (+1.6732650588494815, +0.61034106022517243E-1), (+1.6093364027963906, +0.22463434427155937), (+1.5700344671291311, +0.31482166368160747), (+1.5159355905449878, +0.65145850208935063), (+1.2853807571046290, +0.49529965318975966), (+1.3724008456179058, +0.63922515376241584)

432

433adat = getFFTR(getFFTF(data)) / size(data)

434adat

435(+1.3968930089553437, +0.85170565312914348), (+1.6393241430302603, +0.16058717404769396), (+1.2283514245856857, +0.39822636799664490), (+1.0217494212957094, +0.76089594690443818), (+1.2573921365976157, +0.65084800793290820), (+1.9904319771633843, +0.26093487331342252), (+1.8586582243997509, +0.42831635476098395), (+1.9521141668157149, +0.11954994784959752), (+1.1223615425027391, +0.61663267257183207), (+1.0683963185925194, +0.23541024655030043), (+1.7377975334534768, +0.77609919417268058), (+1.8721491458397606, +0.19729690070511566), (+1.6868431135230262, +0.66130649422446397), (+1.5387331419885746, +0.68489747458973205), (+1.9422204998800465, +0.18010749457763497E-1), (+1.5866304534295006, +0.36652847035100161), (+1.1631441455091855, +0.54703632715029138), (+1.0666563423860831, +0.85006479642421906), (+1.2050783399556237, +0.10115655975689651), (+1.7649487959078589, +0.87325714455776404), (+1.8985253437218055, +0.71413227003353985), (+1.4581035526750066, +0.19606362797248461), (+1.6013346943460371, +0.58170479837877009), (+1.6600930256592179, +0.76669906916998676), (+1.0687537282538049, +0.64113254262316566), (+1.3145922729417270, +0.70303195200922686), (+1.8364503609075475, +0.61355309151825266), (+1.8129613224977428, +0.12783849962164331), (+1.2357781766821700, +0.41177964123228017), (+1.6732650588494822, +0.61034106022517305E-1), (+1.6093364027963908, +0.22463434427155946), (+1.5700344671291309, +0.31482166368160713), (+1.5159355905449876, +0.65145850208935063), (+1.2853807571046290, +0.49529965318975988), (+1.3724008456179064, +0.63922515376241584)

436reltol = sqrt(epsilon(1._TKC))

437reltol

438+0.14901161193847656E-7

439isClose(data, adat, reltol = reltol)

440T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

441call setAsserted(all(isClose(data, adat, reltol = reltol)))

442

443lenData = getUnifRand(5, 100)

444lenData

445+41

446data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

447data

448(+1.08238221747012616052010385985490586, +0.195070901140104357032311292863059801), (+1.15932122120188696253418933099646490, +0.862325804890892780305864956361303024E-1), (+1.36562569847142243821153971295778354, +0.488211092173306857200515230418995333E-1), (+1.52008340711314175778249436821049621, +0.361576432055284543171217183497818879), (+1.77711876894294873231041489731570922, +0.412216408633251308986162693391028108), (+1.85557281316402594822577720794211223, +0.743929732596394028167988949274501045), (+1.83864422571160444249644663679046069, +0.187292458656886969184574917418179150), (+1.33366763026193645301317370492851304, +0.634019006108428074463020297732099693E-1), (+1.86530906374676081223948254320497087, +0.426146455486145016668315165350026692), (+1.73367037567053532887533276967123401, +0.354824062821843002877014327401844173), (+1.68148035811396713204752887040869714, +0.677737611258860056887606824003116159), (+1.66644882023977044247913816061529513, +0.647232242587355069012443428824281704), (+1.16786756918191931295768843481743106, +0.128370190433747751055174942423531772), (+1.58492856138586330255369977230651694, +0.170304326662248417895333268053049124), (+1.59639903977849748457263782125276620, +0.849077567465941602860702354943593369), (+1.83543226222478965831815787223964912, +0.147217873095992401836748459040818979), (+1.34432385031770257081284191572498930, +0.979752153420739921617528991900613937), (+1.63796167050171483899240287347433769, +0.605483836382194520598213626686797163), (+1.11493052009760207751026205576866557, +0.367567689084253670973460324873429385), (+1.48729087913030961021438104390127135, +0.828810831950107317216350009200725801), (+1.12329387871938942237396150707008598, +0.934535058362042048178610713926490684), (+1.41105160427255061435325729863869005, +0.562944989904844665527539306214644823), (+1.47610401417215673140377240594773782, +0.438655783311858188385481247459226704), (+1.68294487698504738557074464055977239, +0.867990063237923440842340322473570891), (+1.02160086906718337085007951869367673, +0.309182802972686040687454230736642857), (+1.99203341923256061127125257583191017, +0.704997734505977063229344525842124723), (+1.66799961548198538814351522863674016, +0.172369487999020023090088989855055580), (+1.36372837589105492676912056768221892, +0.155286951649879160815666599935583279), (+1.04237574301873303010765582382364045, +0.753618192811628617632196558381959489E-1), (+1.13121863112929324635704057607745305, +0.873372678243199925701991667200585741), (+1.09134157496009977557837340919750953, +0.477115216232852455722594379414690187), (+1.99325662021705451412351923434911111, +0.783807417754039549324886189049681226), (+1.76110677764704752954441453850363274, +0.583941858305970993546172745272270329), (+1.73037175744897688471991271389735072, +0.191923201495626995471197033173894174), (+1.28646543998358485848881431058249102, +0.248600274334245565455567865710183896), (+1.01597399040241201669880169183892411, +0.512389349242959615919783110471211719), (+1.15842382387744247232265289676662737, +0.797509047384774909287189558450800454E-1), (+1.05583751631331349281233672331759770, +0.591538000902518607412116345695284520), (+1.08576014883508731900481541014885234, +0.564601518693409923656822250953389401), (+1.04041702966517757044322795461951784, +0.717552863187279302852759678288818764), (+1.72871618541573879739732979942835950, +0.713892251272472640882959390635211127)

449

450adat = getFFTR(getFFTF(data)) / size(data)

451adat

452(+1.08238221747012616052010385985490759, +0.195070901140104357032311292863060331), (+1.15932122120188696253418933099646451, +0.862325804890892780305864956361301339E-1), (+1.36562569847142243821153971295778316, +0.488211092173306857200515230418996777E-1), (+1.52008340711314175778249436821049582, +0.361576432055284543171217183497818927), (+1.77711876894294873231041489731570902, +0.412216408633251308986162693391028301), (+1.85557281316402594822577720794211204, +0.743929732596394028167988949274501045), (+1.83864422571160444249644663679046127, +0.187292458656886969184574917418179078), (+1.33366763026193645301317370492851323, +0.634019006108428074463020297732099332E-1), (+1.86530906374676081223948254320497107, +0.426146455486145016668315165350026692), (+1.73367037567053532887533276967123363, +0.354824062821843002877014327401844558), (+1.68148035811396713204752887040869675, +0.677737611258860056887606824003116159), (+1.66644882023977044247913816061529494, +0.647232242587355069012443428824281704), (+1.16786756918191931295768843481743029, +0.128370190433747751055174942423531724), (+1.58492856138586330255369977230651675, +0.170304326662248417895333268053049149), (+1.59639903977849748457263782125276620, +0.849077567465941602860702354943593658), (+1.83543226222478965831815787223964951, +0.147217873095992401836748459040818787), (+1.34432385031770257081284191572498949, +0.979752153420739921617528991900614034), (+1.63796167050171483899240287347433711, +0.605483836382194520598213626686796874), (+1.11493052009760207751026205576866577, +0.367567689084253670973460324873429433), (+1.48729087913030961021438104390127173, +0.828810831950107317216350009200725898), (+1.12329387871938942237396150707008598, +0.934535058362042048178610713926490877), (+1.41105160427255061435325729863868986, +0.562944989904844665527539306214645208), (+1.47610401417215673140377240594773801, +0.438655783311858188385481247459226753), (+1.68294487698504738557074464055977259, +0.867990063237923440842340322473570891), (+1.02160086906718337085007951869367615, +0.309182802972686040687454230736642569), (+1.99203341923256061127125257583191037, +0.704997734505977063229344525842125012), (+1.66799961548198538814351522863674036, +0.172369487999020023090088989855055387), (+1.36372837589105492676912056768221911, +0.155286951649879160815666599935583375), (+1.04237574301873303010765582382364026, +0.753618192811628617632196558381960091E-1), (+1.13121863112929324635704057607745248, +0.873372678243199925701991667200585645), (+1.09134157496009977557837340919750934, +0.477115216232852455722594379414690283), (+1.99325662021705451412351923434911073, +0.783807417754039549324886189049681226), (+1.76110677764704752954441453850363274, +0.583941858305970993546172745272270425), (+1.73037175744897688471991271389735053, +0.191923201495626995471197033173894174), (+1.28646543998358485848881431058249102, +0.248600274334245565455567865710183944), (+1.01597399040241201669880169183892449, +0.512389349242959615919783110471211623), (+1.15842382387744247232265289676662718, +0.797509047384774909287189558450801538E-1), (+1.05583751631331349281233672331759789, +0.591538000902518607412116345695284617), (+1.08576014883508731900481541014885177, +0.564601518693409923656822250953389305), (+1.04041702966517757044322795461951765, +0.717552863187279302852759678288818860), (+1.72871618541573879739732979942835912, +0.713892251272472640882959390635211127)

453reltol = sqrt(epsilon(1._TKC))

454reltol

455+0.138777878078144567552953958511352539E-16

456isClose(data, adat, reltol = reltol)

457T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

458call setAsserted(all(isClose(data, adat, reltol = reltol)))

459

460lenData = getUnifRand(5, 100)

461lenData

462+51

463data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

464data

465+1.13299203, +1.32206666, +1.29586792, +1.44231200, +1.29413581, +1.97611034, +1.57905817, +1.81162643, +1.26660955, +1.05214381, +1.39819562, +1.47452641, +1.37944698, +1.98470426, +1.67656302, +1.61248302, +1.90227425, +1.81552291, +1.00336623, +1.76474571, +1.85281003, +1.91682982, +1.55661702, +1.22291040, +1.42347288, +1.97415733, +1.78139687, +1.77977645, +1.41995382, +1.24581409, +1.78657436, +1.83890700, +1.68990767, +1.73636699, +1.73291850, +1.99844205, +1.61566710, +1.20686126, +1.84214187, +1.50529981, +1.30440187, +1.71248412, +1.64630795, +1.07283866, +1.41502523, +1.56590700, +1.43821883, +1.78459001, +1.32505918, +1.01110673, +1.46431804

466

467adat = getFFTR(getFFTF(data)) / size(data)

468adat

469+1.13299203, +1.32206666, +1.29586828, +1.44231188, +1.29413593, +1.97611082, +1.57905805, +1.81162632, +1.26660991, +1.05214357, +1.39819586, +1.47452676, +1.37944674, +1.98470378, +1.67656291, +1.61248267, +1.90227437, +1.81552303, +1.00336635, +1.76474547, +1.85281003, +1.91682923, +1.55661738, +1.22291052, +1.42347300, +1.97415686, +1.78139663, +1.77977622, +1.41995370, +1.24581432, +1.78657401, +1.83890712, +1.68990755, +1.73636687, +1.73291838, +1.99844193, +1.61566699, +1.20686162, +1.84214211, +1.50529969, +1.30440176, +1.71248388, +1.64630771, +1.07283890, +1.41502559, +1.56590676, +1.43821871, +1.78459013, +1.32505918, +1.01110685, +1.46431851

470reltol = sqrt(epsilon(1._TKC))

471reltol

472+0.345266977E-3

473isClose(data, adat, reltol = reltol)

474T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

475call setAsserted(all(isClose(data, adat, reltol = reltol)))

476

477lenData = getUnifRand(5, 100)

478lenData

479+11

480data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

481data

482+1.5294656023346789, +1.2958889696148772, +1.9231974433184336, +1.4231090483498217, +1.3197066408573219, +1.7051904344841620, +1.0449883439344889, +1.6502183554708432, +1.8676881434367085, +1.1090906323021332, +1.2949029747044585

483

484adat = getFFTR(getFFTF(data)) / size(data)

485adat

486+1.5294656023346795, +1.2958889696148777, +1.9231974433184342, +1.4231090483498217, +1.3197066408573221, +1.7051904344841615, +1.0449883439344887, +1.6502183554708432, +1.8676881434367083, +1.1090906323021339, +1.2949029747044587

487reltol = sqrt(epsilon(1._TKC))

488reltol

489+0.14901161193847656E-7

490isClose(data, adat, reltol = reltol)

491T, T, T, T, T, T, T, T, T, T, T

492call setAsserted(all(isClose(data, adat, reltol = reltol)))

493

494lenData = getUnifRand(5, 100)

495lenData

496+38

497data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

498data

499+1.07143891171199415265139085233404490, +1.28208317094603682128995349505818238, +1.15169074558801190274742092790257860, +1.02157963973197729764196145132311533, +1.06894285331473384013755832859962890, +1.45171268125051899444639554105037353, +1.60602491700838058721134193641887446, +1.85957220184511756706626148679242140, +1.38699302786985986062278362242182072, +1.06241970207032873278990516209992048, +1.89271592221064396399962484009213517, +1.53850723939099938300399583512195418, +1.56094734311045352099971111057440295, +1.73542864327158394894201576006579743, +1.35934269739404287423021770567947096, +1.82585439440881271746210387866913373, +1.93911326984474943728975176532584422, +1.02575390837248577700197010641389545, +1.87653580951513834006072152267619225, +1.76479720633023676426106006856888172, +1.23375345009598225210346773770227716, +1.41271721762134787081715929867779946, +1.84046069713946293470237072339635425, +1.62504663766732727287092853475361944, +1.87116507135501243347814783823100746, +1.46661228359252909138312034985497903, +1.35455377158280822070444352870890589, +1.50248381663283239524659537537751111, +1.34388399518873564265284210000860325, +1.82133431373764185152862537291792176, +1.90038986418223819233747348037563093, +1.79358213387249158138731787661422232, +1.68285703982097685422878721214770283, +1.43439766620752292127562090514259027, +1.19839306379135498118036004413448971, +1.75022752611444583360414128594671738, +1.74220345376475862896815612299184980, +1.05957222058095511949521387372612578

500

501adat = getFFTR(getFFTF(data)) / size(data)

502adat

503+1.07143891171199415265139085233404451, +1.28208317094603682128995349505818219, +1.15169074558801190274742092790257764, +1.02157963973197729764196145132311475, +1.06894285331473384013755832859962890, +1.45171268125051899444639554105037430, +1.60602491700838058721134193641887427, +1.85957220184511756706626148679242217, +1.38699302786985986062278362242182130, +1.06241970207032873278990516209992029, +1.89271592221064396399962484009213613, +1.53850723939099938300399583512195457, +1.56094734311045352099971111057440411, +1.73542864327158394894201576006579858, +1.35934269739404287423021770567947000, +1.82585439440881271746210387866913411, +1.93911326984474943728975176532584595, +1.02575390837248577700197010641389468, +1.87653580951513834006072152267619070, +1.76479720633023676426106006856888056, +1.23375345009598225210346773770227158, +1.41271721762134787081715929867779426, +1.84046069713946293470237072339635598, +1.62504663766732727287092853475362214, +1.87116507135501243347814783823100804, +1.46661228359252909138312034985497788, +1.35455377158280822070444352870890666, +1.50248381663283239524659537537751208, +1.34388399518873564265284210000860229, +1.82133431373764185152862537291792215, +1.90038986418223819233747348037563266, +1.79358213387249158138731787661422406, +1.68285703982097685422878721214770264, +1.43439766620752292127562090514258950, +1.19839306379135498118036004413449009, +1.75022752611444583360414128594671853, +1.74220345376475862896815612299184884, +1.05957222058095511949521387372612540

504reltol = sqrt(epsilon(1._TKC))

505reltol

506+0.138777878078144567552953958511352539E-16

507isClose(data, adat, reltol = reltol)

508T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

509call setAsserted(all(isClose(data, adat, reltol = reltol)))

510

511

Test:: test_pm_fftpack

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, you must acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library, you must also ask the end users to cite this original ParaMonte library.

Copyright: Computational Data Science Lab

Author:: Fatemeh Bagheri, Tuesday 11:34 PM, August 10, 2021, Dallas, TX

Definition at line 1156 of file pm_fftpack.F90.

The documentation for this interface was generated from the following file:

/home/amir/git/paramonte/src/fortran/main/pm_fftpack.F90